<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt src="https://files.passeidireto.com/33ce9d39-9ba4-40f4-8936-9c985004e9c6/bg1.png" alt="Pré-visualização de imagem de arquivo"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">Livro Eletrônico</div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls0 ws0">Aula 04</div><div class="t m0 x3 h3 y3 ff1 fs1 fc1 sc0 ls0 ws0">Matemática p/ PETROBRAS (Nível médio)</div><div class="t m0 x3 h4 y4 ff2 fs1 fc1 sc0 ls0 ws0">Professor: Arthur Lima</div><div class="t m0 x4 h5 y5 ff2 fs2 fc0 sc0 ls0 ws0">10323012795 - Rosamaria Domingues de Oliveira</div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x5 y6 w2 h6" alt src="https://files.passeidireto.com/33ce9d39-9ba4-40f4-8936-9c985004e9c6/bg2.png" alt="Pré-visualização de imagem de arquivo"><div class="c x0 y0 w1 h0"><div class="t m1 x6 h7 y7 ff3 fs3 fc2 sc0 ls0 ws1"></div></div><div class="c x7 y8 w3 h8"><div class="t m1 x0 h7 y9 ff3 fs3 fc2 sc0 ls0"></div></div><div class="c x0 y0 w1 h0"><div class="t m1 x8 h7 ya ff3 fs3 fc2 sc0 ls0 ws1"></div></div><div class="c x7 yb w3 h9"><div class="t m1 x0 h7 y9 ff3 fs3 fc2 sc0 ls0"></div></div><div class="c x0 y0 w1 h0"><div class="t m1 x9 h7 yc ff3 fs3 fc2 sc0 ls0 ws0"> !</div><div class="t m2 x7 ha yc ff4 fs4 fc3 sc0 ls0"></div><div class="t m3 xa hb yd ff4 fs5 fc2 sc0 ls0"></div><div class="t m4 xb hc ye ff5 fs6 fc3 sc0 ls0"></div><div class="t m4 xb hd yf ff3 fs6 fc4 sc0 ls0 ws2">    </div><div class="t m3 xc hb yf ff4 fs5 fc5 sc0 ls0 ws3"><span class="blank _0"></span></div><div class="t m4 xd hc yf ff5 fs6 fc4 sc0 ls1 ws4"><span class="blank _0"></span><span class="blank _0"></span><span class="ff4 ls0 ws5"><span class="blank _0"></span><span class="ff5 fc3"></span></span></div><div class="t m1 xa he y10 ff6 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 xe hf y11 ff7 fs3 fc3 sc0 ls0 ws0">A<span class="blank _0"></span>UL<span class="blank _1"> </span>A<span class="blank _0"></span> 04:<span class="blank _1"> </span> ANÁ<span class="blank _0"></span>LISE C<span class="blank _1"> </span>OMBINATÓRIA<span class="blank _0"></span> E PR<span class="blank _1"> </span>OBABILIDAD<span class="blank _0"></span>E </div><div class="t m1 xb hf y12 ff7 fs3 fc6 sc0 ls0 ws0"> </div><div class="t m1 xf hf y13 ff7 fs3 fc3 sc0 ls0 ws0">SUMÁRIO <span class="blank _2"> </span>PÁGINA </div><div class="t m1 xb h10 y14 ff8 fs3 fc3 sc0 ls0 ws0">1. Análise Combinató<span class="blank _1"> </span>ri<span class="blank _0"></span>a <span class="blank _3"> </span>01 </div><div class="t m1 xb h10 y15 ff8 fs3 fc3 sc0 ls0 ws0">2. Probabilidade <span class="blank _4"> </span>41 </div><div class="t m1 xb h10 y16 ff8 fs3 fc3 sc0 ls0 ws0">3. Questões apresentadas na <span class="blank _1"> </span>aula <span class="blank _5"> </span>92 </div><div class="t m1 xb h10 y17 ff8 fs3 fc3 sc0 ls0 ws0">4. Gabarito <span class="blank _6"> </span>122 </div><div class="t m1 xb h10 y18 ff8 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 xb h10 y19 ff8 fs3 fc3 sc0 ls0 ws0">Caro aluno, </div><div class="t m1 xb h10 y1a ff8 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 xb hf y1b ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span>Na <span class="blank _8"> </span>aula <span class="blank _8"> </span>de <span class="blank _8"> </span>hoje <span class="blank _8"> </span>trataremos <span class="blank _8"> </span>dos <span class="blank _8"> </span>tópicos <span class="blank _8"> </span>de <span class="blank _8"> </span><span class="ff7">Análise <span class="blank _8"> </span>Combinatória <span class="blank _8"> </span>e </span></div><div class="t m1 xb hf y1c ff7 fs3 fc3 sc0 ls0 ws0">Probabilidade Básica<span class="ff8"> do<span class="blank _1"> </span> seu edital. <span class="blank _0"></span><span class="ff9"> </span></span></div><div class="t m1 xb h11 y1d ff9 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 xb h10 y1e ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span>Bons estudos! </div><div class="t m1 xb h10 y1f ff8 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 xb hf y20 ff7 fs3 fc7 sc0 ls0 ws0">1. Análise Combinatória </div><div class="t m1 xb h10 y21 ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span>Imagine <span class="blank _1"> </span>que <span class="blank _1"> </span>você p<span class="blank _1"> </span>ossui em<span class="blank _1"> </span> seu <span class="blank _1"> </span>armário <span class="blank _1"> </span>3 ca<span class="blank _1"> </span>lças , <span class="blank _1"> </span>4 <span class="blank _1"> </span>camisetas <span class="blank _1"> </span>e 2<span class="blank _1"> </span> pa<span class="blank _1"> </span>res de </div><div class="t m1 xb h10 y22 ff8 fs3 fc3 sc0 ls0 ws0">tênis. <span class="blank _1"> </span>De <span class="blank _1"> </span>quantas m<span class="blank _1"> </span>aneiras d<span class="blank _1"> </span>iferentes você <span class="blank _1"> </span>pod<span class="blank _1"> </span>e se <span class="blank _1"> </span>vestir? <span class="blank _1"> </span>Ora, <span class="blank _1"> </span>basta im<span class="blank _1"> </span>aginar que </div><div class="t m1 xb h10 y23 ff8 fs3 fc3 sc0 ls0 ws0">para <span class="blank _9"> </span>cada <span class="blank _9"> </span>calça <span class="blank _9"> </span>você <span class="blank _a"> </span>pode <span class="blank _9"> </span>utilizar <span class="blank _a"> </span>qualquer <span class="blank _9"> </span>uma <span class="blank _9"> </span>das <span class="blank _9"> </span>4 <span class="blank _9"> </span>camiset<span class="blank _0"></span>as, <span class="blank _9"> </span>e <span class="blank _9"> </span>para <span class="blank _a"> </span>cada </div><div class="t m1 xb h10 y24 ff8 fs3 fc3 sc0 ls0 ws0">conjunto calça-cam<span class="blank _1"> </span>is<span class="blank _0"></span>eta você pode usar qualquer dos 2 p<span class="blank _1"> </span>ares de tênis. </div><div class="t m1 xb h10 y25 ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span>O <span class="blank _b"> </span>princípio <span class="blank _b"> </span>fundamental <span class="blank _b"> </span>da <span class="blank _b"> </span>contagem, <span class="blank _b"> </span>ou<span class="blank _1"> </span> <span class="blank _1"> </span>regra <span class="blank _1"> </span>d<span class="blank _1"> </span>o <span class="blank _1"> </span>prod<span class="blank _1"> </span>uto, <span class="blank _1"> </span>no<span class="blank _1"> </span>s <span class="blank _1"> </span>diz <span class="blank _b"> </span>que <span class="blank _b"> </span>para </div><div class="t m1 xb h10 y26 ff8 fs3 fc3 sc0 ls0 ws0">obter <span class="blank _a"> </span>a <span class="blank _a"> </span>quantida<span class="blank _1"> </span>de <span class="blank _a"> </span>total <span class="blank _a"> </span>de <span class="blank _a"> </span>maneiras <span class="blank _a"> </span>de <span class="blank _a"> </span>se <span class="blank _a"> </span>vestir <span class="blank _a"> </span>basta<span class="blank _1"> </span> <span class="blank _a"> </span>multiplicar <span class="blank _a"> </span>o <span class="blank _a"> </span>número <span class="blank _a"> </span>de </div><div class="t m1 xb h10 y27 ff8 fs3 fc3 sc0 ls0 ws0">calças pelo número de camisa<span class="blank _1"> </span>s e pelo número de tênis, isto é: </div><div class="t m1 x10 h10 y28 ff8 fs3 fc3 sc0 ls0 ws0">Maneiras de se vestir = 3 x 4 x 2 = 24 </div><div class="t m1 xa h10 y29 ff8 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 xb h10 y2a ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span>Em <span class="blank _c"> </span>outras <span class="blank _c"> </span>palavras, <span class="blank _d"> </span>quando <span class="blank _d"> </span>t<span class="blank _1"> </span>emos <span class="blank _d"> </span>acontecimentos <span class="blank _c"> </span>sucessivos <span class="blank _d"> </span>e </div><div class="t m1 xb h10 y2b ff8 fs3 fc3 sc0 ls0 ws0">independentes <span class="blank _e"> </span>(escolha <span class="blank _e"> </span>da<span class="blank _0"></span> <span class="blank _e"> </span>calça, <span class="blank _f"> </span>da <span class="blank _f"> </span>camiseta <span class="blank _f"> </span>e <span class="blank _e"> </span>do <span class="blank _f"> </span>tênis), <span class="blank _f"> </span>b<span class="blank _1"> </span>asta <span class="blank _f"> </span>multiplicarmos <span class="blank _f"> </span>as </div><div class="t m1 xb h10 y2c ff8 fs3 fc3 sc0 ls0 ws0">quantidades <span class="blank _f"> </span>de <span class="blank _1"> </span>po<span class="blank _1"> </span>ssibil<span class="blank _0"></span>idades <span class="blank _f"> </span>de <span class="blank _b"> </span>cada <span class="blank _b"> </span>a<span class="blank _1"> </span>contecimento <span class="blank _b"> </span>(isto <span class="blank _b"> </span>é, <span class="blank _b"> </span>3<span class="blank _1"> </span> <span class="blank _1"> </span>p<span class="blank _1"> </span>ossibilidades <span class="blank _b"> </span>para </div><div class="t m1 xb h10 y2d ff8 fs3 fc3 sc0 ls0 ws0">o <span class="blank _a"> </span>aconte<span class="blank _1"> </span>cimento <span class="blank _a"> </span>“escolha <span class="blank _a"> </span>da <span class="blank _9"> </span>calça”; <span class="blank _a"> </span>4 <span class="blank _a"> </span>para <span class="blank _9"> </span>a <span class="blank _a"> </span>“escolha <span class="blank _9"> </span>da <span class="blank _a"> </span>camiseta” <span class="blank _a"> </span>e <span class="blank _a"> </span>2<span class="blank _1"> </span> <span class="blank _a"> </span>para <span class="blank _a"> </span>a </div><div class="t m1 xb h10 y2e ff8 fs3 fc3 sc0 ls0 ws0">“escolha do tênis”). </div><div class="t m1 x11 h10 y2f ff8 fs3 fc3 sc0 ls0 ws0">Vejamos <span class="blank _9"> </span>um <span class="blank _9"> </span>outro <span class="blank _a"> </span>e<span class="blank _1"> </span>x<span class="blank _0"></span>emp<span class="blank _1"> </span>l<span class="blank _0"></span>o: <span class="blank _9"> </span> <span class="blank _a"> </span>qua<span class="blank _1"> </span>ntos <span class="blank _9"> </span>núm<span class="blank _0"></span>eros <span class="blank _9"> </span>de <span class="blank _9"> </span>3 <span class="blank _9"> </span>algarismos <span class="blank _a"> </span>pod<span class="blank _1"> </span>emos </div><div class="t m1 xb h10 y30 ff8 fs3 fc3 sc0 ls0 ws0">formar utilizando apenas o<span class="blank _1"> </span>s algarismos 1, 2, 3, 4, 5 e 6? </div></div><div class="t m0 x4 h5 y5 ff2 fs2 fc0 sc0 ls0 ws0">10323012795 - Rosamaria Domingues de Oliveira</div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x5 y6 w4 h6" alt src="https://files.passeidireto.com/33ce9d39-9ba4-40f4-8936-9c985004e9c6/bg3.png" alt="Pré-visualização de imagem de arquivo"><div class="c x0 y0 w1 h0"><div class="t m1 x6 h7 y7 ff3 fs3 fc2 sc0 ls0 ws1"></div></div><div class="c x7 y8 w3 h8"><div class="t m1 x0 h7 y9 ff3 fs3 fc2 sc0 ls0"></div></div><div class="c x0 y0 w1 h0"><div class="t m1 x8 h7 ya ff3 fs3 fc2 sc0 ls0 ws1"></div></div><div class="c x7 yb w3 h9"><div class="t m1 x0 h7 y9 ff3 fs3 fc2 sc0 ls0"></div></div><div class="c x0 y0 w1 h0"><div class="t m1 x9 h7 yc ff3 fs3 fc2 sc0 ls0 ws0"> !</div><div class="t m2 x7 ha yc ff4 fs4 fc3 sc0 ls0"></div><div class="t m3 xa hb yd ff4 fs5 fc2 sc0 ls0"></div><div class="t m4 xb hc ye ff5 fs6 fc3 sc0 ls0"></div><div class="t m4 xb hd yf ff3 fs6 fc4 sc0 ls0 ws2">    </div><div class="t m3 xc hb yf ff4 fs5 fc5 sc0 ls0 ws3"><span class="blank _0"></span></div><div class="t m4 xd hc yf ff5 fs6 fc4 sc0 ls1 ws4"><span class="blank _0"></span><span class="blank _0"></span><span class="ff4 ls0 ws5"><span class="blank _0"></span><span class="ff5 fc3"></span></span></div><div class="t m1 x11 h10 y10 ff8 fs3 fc3 sc0 ls0 ws0">Note <span class="blank _b"> </span>que <span class="blank _f"> </span>precisamos <span class="blank _1"> </span>f<span class="blank _1"> </span>ormar <span class="blank _b"> </span>números <span class="blank _b"> </span>co<span class="blank _1"> </span>m <span class="blank _1"> </span>o <span class="blank _b"> </span>f<span class="blank _1"> </span>ormato <span class="blank _b"> </span>“ABC”, <span class="blank _b"> </span>on<span class="blank _1"> </span>de <span class="blank _1"> </span>cada<span class="blank _1"> </span> <span class="blank _1"> </span>le<span class="blank _1"> </span>tra </div><div class="t m1 xb h10 y31 ff8 fs3 fc3 sc0 ls0 ws0">simboliza <span class="blank _e"> </span>um<span class="blank _1"> </span> <span class="blank _f"> </span>a<span class="blank _1"> </span>lgarismo. <span class="blank _e"> </span>Para <span class="blank _e"> </span>a<span class="blank _1"> </span> <span class="blank _e"> </span>posição <span class="blank _e"> </span>A <span class="blank _e"> </span>t<span class="blank _1"> </span>emos <span class="blank _e"> </span>6 <span class="blank _10"> </span>opções <span class="blank _e"> </span>de <span class="blank _e"> </span>a<span class="blank _1"> </span>lgarismos. <span class="blank _e"> </span>Para <span class="blank _e"> </span>a </div><div class="t m1 xb h10 y32 ff8 fs3 fc3 sc0 ls0 ws0">posição <span class="blank _1"> </span>B <span class="blank _1"> </span>temos <span class="blank _1"> </span>novamente <span class="blank _1"> </span>6 o<span class="blank _1"> </span>pções. E<span class="blank _1"> </span> o <span class="blank _1"> </span>mesmo <span class="blank _1"> </span>ocorre <span class="blank _1"> </span>na po<span class="blank _1"> </span>sição C. <span class="blank _1"> </span>Portanto, <span class="blank _1"> </span>a </div><div class="t m1 xb h10 y33 ff8 fs3 fc3 sc0 ls0 ws0">quantidade de números de<span class="blank _1"> </span> 3 algarismos é dada pela multiplicação: </div><div class="t m1 x11 h10 y34 ff8 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 x12 h10 y35 ff8 fs3 fc3 sc0 ls0 ws0">6 x 6 x 6 = 216 possibilidade<span class="blank _1"> </span>s<span class="blank _0"></span> </div><div class="t m1 x13 h10 y36 ff8 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 x11 h10 y37 ff8 fs3 fc3 sc0 ls0 ws0">E <span class="blank _f"> </span>se <span class="blank _1"> </span>o<span class="blank _1"> </span> <span class="blank _1"> </span>e<span class="blank _1"> </span>xercí<span class="blank _0"></span>cio <span class="blank _f"> </span>dissesse <span class="blank _b"> </span>que <span class="blank _f"> </span>os <span class="blank _b"> </span>números <span class="blank _b"> </span>de <span class="blank _f"> </span>3 <span class="blank _b"> </span>algarismos <span class="blank _f"> </span>formados <span class="blank _b"> </span>devem </div><div class="t m1 xb h10 y38 ff8 fs3 fc3 sc0 ls0 ws0">ter <span class="blank _11"> </span>os <span class="blank _11"> </span>3 <span class="blank _11"> </span>algarismos <span class="blank _11"> </span>distintos? <span class="blank _11"> </span>Neste <span class="blank _11"> </span>caso, <span class="blank _11"> </span>teríamos <span class="blank _11"> </span>também <span class="blank _11"> </span>6 <span class="blank _11"> </span>opções <span class="blank _11"> </span>para </div><div class="t m1 xb h10 y39 ff8 fs3 fc3 sc0 ls0 ws0">preencher <span class="blank _9"> </span>a <span class="blank _a"> </span>posição <span class="blank _a"> </span>A. <span class="blank _a"> </span>P<span class="blank _1"> </span>ara <span class="blank _a"> </span>preencher <span class="blank _a"> </span>a <span class="blank _a"> </span>posiçã<span class="blank _1"> </span>o <span class="blank _a"> </span>B, <span class="blank _a"> </span>não <span class="blank _a"> </span>mais <span class="blank _a"> </span>po<span class="blank _1"> </span>demos <span class="blank _a"> </span>usar <span class="blank _a"> </span>o </div><div class="t m1 xb h10 y3a ff8 fs3 fc3 sc0 ls0 ws0">número <span class="blank _f"> </span>que <span class="blank _f"> </span>já <span class="blank _f"> </span>fo<span class="blank _1"> </span>i <span class="blank _f"> </span>utilizado <span class="blank _f"> </span>para <span class="blank _f"> </span>A. <span class="blank _f"> </span>Portanto, <span class="blank _f"> </span>temos <span class="blank _f"> </span>5 <span class="blank _f"> </span>op<span class="blank _1"> </span>ções. <span class="blank _f"> </span>E <span class="blank _f"> </span>para <span class="blank _f"> </span>a <span class="blank _f"> </span>posição <span class="blank _f"> </span>C, </div><div class="t m1 xb h10 y3b ff8 fs3 fc3 sc0 ls0 ws0">restam apenas 4 opções. A<span class="blank _1"> </span>ssim, terí<span class="blank _0"></span>amos: </div><div class="t m1 x11 h10 y3c ff8 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 x12 h10 y3d ff8 fs3 fc3 sc0 ls0 ws0">6 x 5 x 4 = 120 possibilidade<span class="blank _1"> </span>s<span class="blank _0"></span> </div><div class="t m1 x13 h10 y3e ff8 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 x11 h10 y3f ff8 fs3 fc3 sc0 ls0 ws0">E <span class="blank _1"> </span>se <span class="blank _1"> </span>o <span class="blank _1"> </span>exercício <span class="blank _1"> </span>houvesse <span class="blank _1"> </span>dito <span class="blank _1"> </span>que, <span class="blank _1"> </span>além<span class="blank _1"> </span> de <span class="blank _1"> </span>forma<span class="blank _1"> </span>r núme<span class="blank _1"> </span>ros <span class="blank _1"> </span>com algarismos </div><div class="t m1 xb h10 y40 ff8 fs3 fc3 sc0 ls0 ws0">distintos, o algarismo 2 sempre de<span class="blank _1"> </span>ve <span class="blank _12"> </span>estar presente? Ora, precisamos calcular </div><div class="t m1 xb h10 y41 ff8 fs3 fc3 sc0 ls0 ws0">quantos <span class="blank _f"> </span>números <span class="blank _f"> </span>podemos <span class="blank _f"> </span>formar <span class="blank _b"> </span>tendo<span class="blank _1"> </span> <span class="blank _b"> </span>o <span class="blank _f"> </span>2 <span class="blank _f"> </span>na <span class="blank _b"> </span>po<span class="blank _1"> </span>sição <span class="blank _b"> </span>A, <span class="blank _f"> </span>depois <span class="blank _f"> </span>na <span class="blank _f"> </span>posição <span class="blank _f"> </span>B, <span class="blank _b"> </span>e </div><div class="t m1 xb h10 y42 ff8 fs3 fc3 sc0 ls0 ws0">depois na posição C. </div><div class="t m1 x11 h10 y43 ff8 fs3 fc3 sc0 ls0 ws0">Se <span class="blank _b"> </span>o <span class="blank _1"> </span>2<span class="blank _1"> </span> <span class="blank _1"> </span>estiver <span class="blank _1"> </span>n<span class="blank _1"> </span>a <span class="blank _1"> </span>pos<span class="blank _1"> </span>i<span class="blank _0"></span>ção <span class="blank _b"> </span>A, <span class="blank _b"> </span>teremos <span class="blank _b"> </span>números <span class="blank _b"> </span>do <span class="blank _1"> </span>tip<span class="blank _1"> </span>o <span class="blank _1"> </span>“2BC”. <span class="blank _b"> </span>Para <span class="blank _b"> </span>a <span class="blank _b"> </span>posição </div><div class="t m1 xb h10 y44 ff8 fs3 fc3 sc0 ls0 ws0">B <span class="blank _1"> </span>temo<span class="blank _1"> </span>s<span class="blank _0"></span> <span class="blank _1"> </span>5 <span class="blank _1"> </span>o<span class="blank _1"> </span>pções <span class="blank _1"> </span>de <span class="blank _1"> </span>algarismos, <span class="blank _1"> </span>pois <span class="blank _1"> </span>o <span class="blank _b"> </span>2 <span class="blank _1"> </span>já <span class="blank _1"> </span>foi <span class="blank _1"> </span>utilizado. <span class="blank _b"> </span>E <span class="blank _1"> </span>para <span class="blank _1"> </span>a <span class="blank _1"> </span>posiçã<span class="blank _1"> </span>o <span class="blank _1"> </span>C <span class="blank _1"> </span>temos </div><div class="t m1 xb h10 y45 ff8 fs3 fc3 sc0 ls0 ws0">4 <span class="blank _b"> </span>opções. <span class="blank _b"> </span>Portanto, <span class="blank _b"> </span>teremos <span class="blank _b"> </span>1 <span class="blank _b"> </span>x <span class="blank _1"> </span>5<span class="blank _1"> </span> <span class="blank _1"> </span>x <span class="blank _b"> </span>4 <span class="blank _b"> </span>= <span class="blank _1"> </span>2<span class="blank _1"> </span>0 <span class="blank _1"> </span>po<span class="blank _1"> </span>ssibilidades <span class="blank _1"> </span>de<span class="blank _1"> </span> <span class="blank _1"> </span>números <span class="blank _1"> </span>d<span class="blank _1"> </span>o <span class="blank _1"> </span>tipo <span class="blank _b"> </span>2BC. </div><div class="t m1 xb h10 y46 ff8 fs3 fc3 sc0 ls0 ws0">Analogamente, <span class="blank _10"> </span>para <span class="blank _e"> </span>núm<span class="blank _1"> </span>eros <span class="blank _e"> </span>do <span class="blank _e"> </span>tip<span class="blank _1"> </span>o <span class="blank _e"> </span>“A2C”, <span class="blank _e"> </span>t<span class="blank _1"> </span>emos <span class="blank _e"> </span>5 <span class="blank _10"> </span>x <span class="blank _e"> </span>1<span class="blank _1"> </span> <span class="blank _e"> </span>x <span class="blank _e"> </span>4 <span class="blank _10"> </span>= <span class="blank _10"> </span>20 <span class="blank _10"> </span>possibilidades. </div><div class="t m1 xb h10 y47 ff8 fs3 fc3 sc0 ls0 ws0">Temos outras <span class="blank _1"> </span>20 possibilidades para n<span class="blank _1"> </span>úmeros do tipo “AB2<span class="blank _1"> </span>”. Ou seja, ao <span class="blank _1"> </span>todo temos </div><div class="t m1 xb h10 y48 ff8 fs3 fc3 sc0 ls0 ws0">60 possibilidades. </div><div class="t m1 x11 h10 y49 ff8 fs3 fc3 sc0 ls0 ws0">Você <span class="blank _10"> </span>reparou<span class="blank _1"> </span> <span class="blank _e"> </span>que <span class="blank _13"> </span>nos <span class="blank _10"> </span>exemplos <span class="blank _10"> </span>a<span class="blank _1"> </span>nteriores <span class="blank _e"> </span>nós <span class="blank _13"> </span>haviamos <span class="blank _10"> </span>efetuado <span class="blank _13"> </span>apenas </div><div class="t m1 xb h10 y4a ff8 fs3 fc3 sc0 ls0 ws0">multiplicações para chegar no<span class="blank _1"> </span> resultado, e neste último e<span class="blank _1"> </span>xemplo fo<span class="blank _0"></span>i preciso ef<span class="blank _1"> </span>etuar a </div><div class="t m1 xb h10 y4b ff8 fs3 fc3 sc0 ls0 ws0">soma 20 + 20 + 2<span class="blank _1"> </span>0? Uma dica para você saber quando<span class="blank _1"> </span> somar e quando multiplicar é </div><div class="t m1 xb h10 y4c ff8 fs3 fc3 sc0 ls0 ws0">perceber a presença das e<span class="blank _1"> </span>xpressões “E” e “OU”<span class="blank _0"></span>. Veja <span class="blank _1"> </span>como <span class="blank _0"></span>fa<span class="blank _1"> </span>z<span class="blank _0"></span>er isso: </div><div class="t m1 xb h10 y4d ff8 fs3 fc3 sc0 ls0 ws0">- <span class="blank _9"> </span>n<span class="blank _1"> </span>o <span class="blank _9"> </span>exemplo <span class="blank _12"> </span>das <span class="blank _12"> </span>c<span class="blank _0"></span>amisetas, <span class="blank _12"> </span>calças <span class="blank _9"> </span>e <span class="blank _12"> </span>tênis, <span class="blank _9"> </span>tínhamo<span class="blank _1"> </span>s <span class="blank _9"> </span>4 <span class="blank _12"> </span>possibil<span class="blank _0"></span>idades <span class="blank _12"> </span>para <span class="blank _9"> </span>a<span class="blank _1"> </span>s<span class="blank _0"></span> </div><div class="t m1 xb h10 y4e ff8 fs3 fc3 sc0 ls0 ws0">camisetas <span class="blank _e"> </span>E<span class="blank _1"> </span> <span class="blank _f"> </span>3<span class="blank _1"> </span> <span class="blank _f"> </span>possib<span class="blank _1"> </span>i<span class="blank _0"></span>lidades <span class="blank _10"> </span>para <span class="blank _e"> </span>as <span class="blank _e"> </span>calças <span class="blank _e"> </span>E <span class="blank _10"> </span>2 <span class="blank _e"> </span>possib<span class="blank _1"> </span>ilid<span class="blank _0"></span>ades <span class="blank _e"> </span>para <span class="blank _e"> </span>o<span class="blank _1"> </span>s <span class="blank _e"> </span>tênis. <span class="blank _e"> </span>Por </div><div class="t m1 xb h10 y4f ff8 fs3 fc3 sc0 ls0 ws0">isso, multiplicamos 4 x 3 x 2. </div><div class="t m1 xb h10 y50 ff8 fs3 fc3 sc0 ls0 ws0">- <span class="blank _1"> </span>para <span class="blank _1"> </span>f<span class="blank _1"> </span>ormar <span class="blank _1"> </span>números <span class="blank _1"> </span>de <span class="blank _b"> </span>3 <span class="blank _1"> </span>algarismos <span class="blank _1"> </span>dist<span class="blank _1"> </span>intos <span class="blank _1"> </span>com <span class="blank _1"> </span>os <span class="blank _1"> </span>eleme<span class="blank _1"> </span>ntos <span class="blank _1"> </span>{1, <span class="blank _1"> </span>2, <span class="blank _1"> </span>3, <span class="blank _b"> </span>4, <span class="blank _1"> </span>5, <span class="blank _1"> </span>6}, </div><div class="t m1 xb h10 y51 ff8 fs3 fc3 sc0 ls0 ws0">tínhamos 6 possibilidades para o primeiro algarismo E 5 possibilidade<span class="blank _1"> </span>s p<span class="blank _0"></span>ara o </div></div><div class="t m0 x4 h5 y5 ff2 fs2 fc0 sc0 ls0 ws0">10323012795 - Rosamaria Domingues de Oliveira</div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x5 y6 w4 h6" alt src="https://files.passeidireto.com/33ce9d39-9ba4-40f4-8936-9c985004e9c6/bg4.png" alt="Pré-visualização de imagem de arquivo"><div class="c x0 y0 w1 h0"><div class="t m1 x6 h7 y7 ff3 fs3 fc2 sc0 ls0 ws1"></div></div><div class="c x7 y8 w3 h8"><div class="t m1 x0 h7 y9 ff3 fs3 fc2 sc0 ls0"></div></div><div class="c x0 y0 w1 h0"><div class="t m1 x8 h7 ya ff3 fs3 fc2 sc0 ls0 ws1"></div></div><div class="c x7 yb w3 h9"><div class="t m1 x0 h7 y9 ff3 fs3 fc2 sc0 ls0"></div></div><div class="c x0 y0 w1 h0"><div class="t m1 x9 h7 yc ff3 fs3 fc2 sc0 ls0 ws0"> !</div><div class="t m2 x7 ha yc ff4 fs4 fc3 sc0 ls0"></div><div class="t m3 xa hb yd ff4 fs5 fc2 sc0 ls0"></div><div class="t m4 xb hc ye ff5 fs6 fc3 sc0 ls0"></div><div class="t m4 xb hd yf ff3 fs6 fc4 sc0 ls0 ws2">    </div><div class="t m3 xc hb yf ff4 fs5 fc5 sc0 ls0 ws3"><span class="blank _0"></span></div><div class="t m4 xd hc yf ff5 fs6 fc4 sc0 ls1 ws4"><span class="blank _0"></span><span class="blank _0"></span><span class="ff4 ls0 ws5"><span class="blank _0"></span><span class="ff5 fc3"></span></span></div><div class="t m1 xb h10 y10 ff8 fs3 fc3 sc0 ls0 ws0">segundo <span class="blank _e"> </span>E <span class="blank _f"> </span>4 <span class="blank _e"> </span>possibilida<span class="blank _1"> </span>des <span class="blank _f"> </span>para <span class="blank _e"> </span>o <span class="blank _f"> </span>te<span class="blank _1"> </span>rceiro, <span class="blank _f"> </span>de <span class="blank _e"> </span>modo <span class="blank _e"> </span>que <span class="blank _f"> </span>novamente <span class="blank _e"> </span>efetuamos <span class="blank _e"> </span>a </div><div class="t m1 xb h10 y31 ff8 fs3 fc3 sc0 ls0 ws0">multiplicação 6 x 5 x 4. </div><div class="t m1 xb h10 y32 ff8 fs3 fc3 sc0 ls0 ws0">- <span class="blank _9"> </span>já <span class="blank _9"> </span>para <span class="blank _9"> </span>obter <span class="blank _9"> </span>números <span class="blank _9"> </span>de <span class="blank _9"> </span>3 <span class="blank _9"> </span>algarismos <span class="blank _9"> </span>distintos <span class="blank _9"> </span>onde <span class="blank _9"> </span>o <span class="blank _9"> </span>2 <span class="blank _9"> </span>estivesse <span class="blank _9"> </span>presente, </div><div class="t m1 xb h10 y33 ff8 fs3 fc3 sc0 ls0 ws0">vimos <span class="blank _9"> </span>que <span class="blank _a"> </span>o <span class="blank _9"> </span>2 <span class="blank _9"> </span>podia <span class="blank _a"> </span>e<span class="blank _1"> </span>star <span class="blank _a"> </span>na<span class="blank _1"> </span> <span class="blank _a"> </span>primeira <span class="blank _9"> </span>posição <span class="blank _a"> </span>OU <span class="blank _9"> </span>na <span class="blank _9"> </span>segunda <span class="blank _9"> </span>posição <span class="blank _a"> </span>O<span class="blank _1"> </span>U <span class="blank _a"> </span>na </div><div class="t m1 xb h10 y34 ff8 fs3 fc3 sc0 ls0 ws0">terceira <span class="blank _1"> </span>posição. <span class="blank _1"> </span>Foi por <span class="blank _1"> </span>isso <span class="blank _1"> </span>que <span class="blank _1"> </span>tivemos que<span class="blank _1"> </span> somar <span class="blank _1"> </span>as <span class="blank _1"> </span>20 <span class="blank _1"> </span>possibilidades <span class="blank _1"> </span>de t<span class="blank _1"> </span>er o <span class="blank _1"> </span>2 </div><div class="t m1 xb h10 y35 ff8 fs3 fc3 sc0 ls0 ws0">na <span class="blank _10"> </span>primeira <span class="blank _10"> </span>p<span class="blank _1"> </span>osição <span class="blank _e"> </span>co<span class="blank _1"> </span>m <span class="blank _10"> </span>as <span class="blank _e"> </span>2<span class="blank _1"> </span>0 <span class="blank _10"> </span>possibilidades <span class="blank _10"> </span>de <span class="blank _10"> </span>e<span class="blank _1"> </span>le <span class="blank _e"> </span>esta<span class="blank _1"> </span>r <span class="blank _e"> </span>na <span class="blank _13"> </span>segunda <span class="blank _10"> </span>posição <span class="blank _10"> </span>e </div><div class="t m1 xb h10 y36 ff8 fs3 fc3 sc0 ls0 ws0">com as 20 possibilidades d<span class="blank _1"> </span>e ele estar na terceira posição. </div><div class="t m1 xb h10 y37 ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span>Lembrando-se <span class="blank _a"> </span>que <span class="blank _a"> </span>o <span class="blank _13"> </span>“E” <span class="blank _a"> </span>remete <span class="blank _a"> </span>à <span class="blank _13"> </span>multiplicaçã<span class="blank _1"> </span>o <span class="blank _13"> </span>e <span class="blank _a"> </span>o <span class="blank _13"> </span>“OU” <span class="blank _a"> </span>remete <span class="blank _a"> </span>à <span class="blank _13"> </span>soma, </div><div class="t m1 xb h10 y38 ff8 fs3 fc3 sc0 ls0 ws0">você <span class="blank _11"> </span>dif<span class="blank _1"> </span>icilmente <span class="blank _8"> </span>err<span class="blank _0"></span>ará <span class="blank _11"> </span>u<span class="blank _1"> </span>ma <span class="blank _11"> </span>questão. <span class="blank _8"> </span>Em <span class="blank _11"> </span>uma <span class="blank _8"> </span>abordagem <span class="blank _11"> </span>mais <span class="blank _8"> </span>acadêmica, </div><div class="t m1 xb h10 y52 ff8 fs3 fc3 sc0 ls0 ws0">dizemos que: </div><div class="t m1 xb h10 y53 ff8 fs3 fc3 sc0 ls0 ws0">- <span class="blank _b"> </span>o <span class="blank _f"> </span>princípio <span class="blank _b"> </span>m<span class="blank _1"> </span>ultiplicativo <span class="blank _b"> </span>é <span class="blank _f"> </span>utilizado <span class="blank _f"> </span>no <span class="blank _b"> </span>ca<span class="blank _1"> </span>so <span class="blank _b"> </span>de<span class="blank _1"> </span> <span class="blank _b"> </span>eventos <span class="blank _f"> </span>independentes <span class="blank _f"> </span>(a <span class="blank _b"> </span>e<span class="blank _1"> </span>scolh<span class="blank _0"></span>a </div><div class="t m1 xb h10 y54 ff8 fs3 fc3 sc0 ls0 ws0">da camiseta independe d<span class="blank _1"> </span>a escolha da calça, que independe da escolha do tênis); </div><div class="t m1 xb h10 y55 ff8 fs3 fc3 sc0 ls0 ws0">- <span class="blank _9"> </span>o<span class="blank _1"> </span> <span class="blank _9"> </span>princípio <span class="blank _12"> </span>aditivo <span class="blank _9"> </span>é <span class="blank _12"> </span>utilizado <span class="blank _9"> </span>no <span class="blank _12"> </span>caso <span class="blank _9"> </span>de <span class="blank _12"> </span>eventos <span class="blank _9"> </span>mutu<span class="blank _1"> </span>amente <span class="blank _9"> </span>excludentes <span class="blank _12"> </span>(a </div><div class="t m1 xb h10 y56 ff8 fs3 fc3 sc0 ls0 ws0">presença <span class="blank _9"> </span>d<span class="blank _1"> </span>o <span class="blank _9"> </span>2 <span class="blank _9"> </span>em<span class="blank _1"> </span> <span class="blank _a"> </span>uma<span class="blank _1"> </span> <span class="blank _9"> </span>posição <span class="blank _9"> </span>e<span class="blank _1"> </span>xcl<span class="blank _0"></span>ui <span class="blank _9"> </span>a<span class="blank _1"> </span> <span class="blank _9"> </span>possibilidade <span class="blank _12"> </span>de <span class="blank _9"> </span>ele <span class="blank _9"> </span>estar <span class="blank _12"> </span>nas <span class="blank _9"> </span>demais </div><div class="t m1 xb h10 y57 ff8 fs3 fc3 sc0 ls0 ws0">posições); </div><div class="t m1 x11 h10 y58 ff8 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 x11 h10 y59 ff8 fs3 fc3 sc0 ls0 ws0">Sobre este assunto, tente <span class="blank _1"> </span>resolv<span class="blank _0"></span>er a questã<span class="blank _1"> </span>o <span class="blank _0"></span>a seguir: </div><div class="t m1 xb hf y5a ff7 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 xb hf y5b ff7 fs3 fc3 sc0 ls0 ws0">1. <span class="blank _a"> </span>ESAF <span class="blank _13"> </span>– <span class="blank _a"> </span>STN <span class="blank _13"> </span>–<span class="blank _1"> </span> <span class="blank _13"> </span>20<span class="blank _1"> </span>08) <span class="blank _a"> </span><span class="ff8 fc8">Ana <span class="blank _13"> </span>p<span class="blank _1"> </span>ossui <span class="blank _13"> </span>em<span class="blank _1"> </span> <span class="blank _13"> </span>seu <span class="blank _a"> </span><span class="ff9">closed <span class="blank _a"> </span></span>90 <span class="blank _a"> </span>pares <span class="blank _13"> </span>de <span class="blank _a"> </span>sapatos, <span class="blank _a"> </span>todos </span></div><div class="t m1 xb h10 y5c ff8 fs3 fc8 sc0 ls0 ws0">devidamente <span class="blank _11"> </span>acondicionados <span class="blank _11"> </span>em <span class="blank _11"> </span>caixas <span class="blank _11"> </span>numeradas <span class="blank _11"> </span>de <span class="blank _11"> </span>1<span class="blank _0"></span> <span class="blank _11"> </span>a <span class="blank _11"> </span>90. <span class="blank _11"> </span>Beatriz<span class="blank _0"></span> <span class="blank _11"> </span>pede </div><div class="t m1 xb h10 y5d ff8 fs3 fc8 sc0 ls0 ws0">emprestado <span class="blank _10"> </span>à <span class="blank _e"> </span>An<span class="blank _1"> </span>a <span class="blank _e"> </span>quatro <span class="blank _10"> </span>pares <span class="blank _e"> </span>d<span class="blank _1"> </span>e <span class="blank _e"> </span>sapatos. <span class="blank _e"> </span>A<span class="blank _1"> </span>tendendo <span class="blank _e"> </span>ao <span class="blank _10"> </span>pedido <span class="blank _10"> </span>da <span class="blank _e"> </span>a<span class="blank _1"> </span>miga, <span class="blank _e"> </span>Ana </div><div class="t m1 xb h10 y5e ff8 fs3 fc8 sc0 ls0 ws0">retira <span class="blank _1"> </span>do <span class="blank _1"> </span><span class="ff9">closed <span class="blank _1"> </span></span>quatro <span class="blank _1"> </span>caixas <span class="blank _1"> </span>de <span class="blank _1"> </span>sapatos. <span class="blank _1"> </span>O n<span class="blank _1"> </span>úmero <span class="blank _1"> </span>de <span class="blank _1"> </span>retiradas <span class="blank _1"> </span>possív<span class="blank _0"></span>eis <span class="blank _1"> </span>que <span class="blank _1"> </span>Ana </div><div class="t m1 xb h10 y5f ff8 fs3 fc8 sc0 ls0 ws0">pode realizar de modo que a terceira c<span class="blank _1"> </span>aixa retir<span class="blank _0"></span>ada se<span class="blank _1"> </span>ja a de número 20 é igual a: </div><div class="t m1 xb h10 y60 ff8 fs3 fc8 sc0 ls0 ws0">a) 681384 </div><div class="t m1 xb h10 y61 ff8 fs3 fc8 sc0 ls0 ws0">b) 382426 </div><div class="t m1 xb h10 y62 ff8 fs3 fc8 sc0 ls0 ws0">c) 43262 </div><div class="t m1 xb h10 y63 ff8 fs3 fc8 sc0 ls0 ws0">d) 7488 </div><div class="t m1 xb h10 y64 ff8 fs3 fc8 sc0 ls0 ws0">e) 2120 </div><div class="t m1 xb hf y65 ff7 fs3 fc8 sc0 ls0 ws0">RESOLUÇÃO: </div><div class="t m1 xb hf y66 ff7 fs3 fc8 sc0 ls2 ws0"> <span class="ff8 ls0">Queremos <span class="blank _e"> </span>que <span class="blank _f"> </span>a <span class="blank _f"> </span>3ª <span class="blank _e"> </span>caixa <span class="blank _f"> </span>seja <span class="blank _f"> </span>a <span class="blank _f"> </span>d<span class="blank _1"> </span>e <span class="blank _f"> </span>número <span class="blank _f"> </span>20. <span class="blank _f"> </span>Assim, <span class="blank _e"> </span>ao <span class="blank _f"> </span>retirar <span class="blank _f"> </span>a <span class="blank _e"> </span>primeira </span></div><div class="t m1 xb h10 y67 ff8 fs3 fc8 sc0 ls0 ws0">caixa, <span class="blank _f"> </span>podemos <span class="blank _f"> </span>pegar <span class="blank _f"> </span>qualquer <span class="blank _f"> </span>uma <span class="blank _f"> </span>das <span class="blank _f"> </span>90 <span class="blank _f"> </span>caixas, <span class="blank _f"> </span>exceto <span class="blank _f"> </span>a <span class="blank _f"> </span>de <span class="blank _f"> </span>número <span class="blank _f"> </span>20. <span class="blank _b"> </span>Lo<span class="blank _1"> </span>go,<span class="blank _0"></span> </div><div class="t m1 xb h10 y68 ff8 fs3 fc8 sc0 ls0 ws0">existem <span class="blank _13"> </span>89 <span class="blank _13"> </span>ca<span class="blank _1"> </span>ix<span class="blank _0"></span>as <span class="blank _13"> </span>que<span class="blank _1"> </span> <span class="blank _10"> </span>po<span class="blank _1"> </span>dem <span class="blank _13"> </span>ser <span class="blank _13"> </span>pegas <span class="blank _13"> </span>na <span class="blank _13"> </span>1ª <span class="blank _13"> </span>te<span class="blank _1"> </span>ntativa, <span class="blank _10"> </span>ob<span class="blank _1"> </span>edecendo <span class="blank _10"> </span>a <span class="blank _13"> </span>re<span class="blank _1"> </span>gra <span class="blank _10"> </span>do </div><div class="t m1 xb h10 y69 ff8 fs3 fc8 sc0 ls0 ws0">enunciado. </div></div><div class="t m0 x4 h5 y5 ff2 fs2 fc0 sc0 ls0 ws0">10323012795 - Rosamaria Domingues de Oliveira</div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x5 y6 w2 h6" alt src="https://files.passeidireto.com/33ce9d39-9ba4-40f4-8936-9c985004e9c6/bg5.png" alt="Pré-visualização de imagem de arquivo"><div class="c x0 y0 w1 h0"><div class="t m1 x6 h7 y7 ff3 fs3 fc2 sc0 ls0 ws1"></div></div><div class="c x7 y8 w3 h8"><div class="t m1 x0 h7 y9 ff3 fs3 fc2 sc0 ls0"></div></div><div class="c x0 y0 w1 h0"><div class="t m1 x8 h7 ya ff3 fs3 fc2 sc0 ls0 ws1"></div></div><div class="c x7 yb w3 h9"><div class="t m1 x0 h7 y9 ff3 fs3 fc2 sc0 ls0"></div></div><div class="c x0 y0 w1 h0"><div class="t m1 x9 h7 yc ff3 fs3 fc2 sc0 ls0 ws0"> !</div><div class="t m2 x7 ha yc ff4 fs4 fc3 sc0 ls0"></div><div class="t m3 xa hb yd ff4 fs5 fc2 sc0 ls0"></div><div class="t m4 xb hc ye ff5 fs6 fc3 sc0 ls0"></div><div class="t m4 xb hd yf ff3 fs6 fc4 sc0 ls0 ws2">    </div><div class="t m3 xc hb yf ff4 fs5 fc5 sc0 ls0 ws3"><span class="blank _0"></span></div><div class="t m4 xd hc yf ff5 fs6 fc4 sc0 ls1 ws4"><span class="blank _0"></span><span class="blank _0"></span><span class="ff4 ls0 ws5"><span class="blank _0"></span><span class="ff5 fc3"></span></span></div><div class="t m1 xb h10 y10 ff8 fs3 fc8 sc0 ls0 ws0"> <span class="blank _7"> </span>No <span class="blank _b"> </span>m<span class="blank _1"> </span>omento <span class="blank _b"> </span>d<span class="blank _1"> </span>e <span class="blank _b"> </span>retirar <span class="blank _f"> </span>a <span class="blank _b"> </span>2ª <span class="blank _f"> </span>caixa, <span class="blank _b"> </span>veja <span class="blank _f"> </span>que <span class="blank _f"> </span>não <span class="blank _b"> </span>podem<span class="blank _1"> </span>os <span class="blank _b"> </span>obter <span class="blank _f"> </span>nem <span class="blank _b"> </span>a <span class="blank _f"> </span>caixa </div><div class="t m1 xb h10 y31 ff8 fs3 fc8 sc0 ls0 ws0">20 <span class="blank _14"> </span>e <span class="blank _14"> </span>nem <span class="blank _14"> </span>a <span class="blank _15"> </span>caixa <span class="blank _15"> </span>que<span class="blank _1"> </span> <span class="blank _15"> </span>já <span class="blank _15"> </span>fo<span class="blank _1"> </span>i <span class="blank _15"> </span>eliminada <span class="blank _15"> </span>na <span class="blank _14"> </span>1ª <span class="blank _14"> </span>tentativa. <span class="blank _15"> </span>Temos, <span class="blank _14"> </span>portanto, <span class="blank _14"> </span>88 </div><div class="t m1 xb h10 y32 ff8 fs3 fc8 sc0 ls0 ws0">possibilidades restantes. </div><div class="t m1 xb h10 y6a ff8 fs3 fc8 sc0 ls0 ws0"> <span class="blank _7"> </span>Para <span class="blank _13"> </span>a<span class="blank _1"> </span> <span class="blank _10"> </span>3ª <span class="blank _a"> </span>retirada <span class="blank _13"> </span>só <span class="blank _13"> </span>t<span class="blank _1"> </span>emos <span class="blank _13"> </span>uma <span class="blank _13"> </span>po<span class="blank _1"> </span>ssibilidade <span class="blank _13"> </span>que <span class="blank _13"> </span>atende <span class="blank _a"> </span>o <span class="blank _13"> </span>enunciado: <span class="blank _13"> </span>a </div><div class="t m1 xb h10 y6b ff8 fs3 fc8 sc0 ls0 ws0">caixa <span class="blank _16"> </span>20. <span class="blank _16"> </span>Já <span class="blank _16"> </span>para <span class="blank _16"> </span>a <span class="blank _16"> </span>4ª <span class="blank _16"> </span>retirada, <span class="blank _16"> </span>podemos <span class="blank _16"> </span>pegar <span class="blank _16"> </span>qualquer <span class="blank _16"> </span>uma <span class="blank _16"> </span>das <span class="blank _16"> </span>87 <span class="blank _16"> </span>caixas </div><div class="t m1 xb h10 y6c ff8 fs3 fc8 sc0 ls0 ws0">restantes. Veja isso <span class="blank _1"> </span>r<span class="blank _0"></span>esumido na tabela abaixo: </div><div class="t m1 x14 he y6d ff6 fs3 fc8 sc0 ls0 ws0">Retirada 1 <span class="blank _17"> </span>Retirada 2 <span class="blank _17"> </span>Retirada 3 <span class="blank _18"> </span>Retirada 4 </div><div class="t m1 x15 h10 y6e ff8 fs3 fc8 sc0 ls3 ws0">89 </div><div class="t m1 x15 h10 y6f ff8 fs3 fc8 sc0 ls0 ws0">possibilidades </div><div class="t m1 x15 h10 y70 ff8 fs3 fc8 sc0 ls0 ws0">(pois <span class="blank _19"> </span>a <span class="blank _19"> </span>caixa </div><div class="t m1 x15 h10 y71 ff8 fs3 fc8 sc0 ls0 ws0">20 <span class="blank _1a"> </span>não <span class="blank _1a"> </span>pode </div><div class="t m1 x15 h10 y72 ff8 fs3 fc8 sc0 ls0 ws0">estar <span class="blank _14"> </span>aqui, <span class="blank _14"> </span>só </div><div class="t m1 x15 h10 y73 ff8 fs3 fc8 sc0 ls0 ws0">na retirada 3) </div><div class="t m1 x12 h10 y74 ff8 fs3 fc8 sc0 ls4 ws0">88 </div><div class="t m1 x16 h10 y75 ff8 fs3 fc8 sc0 ls0 ws0">possibilidades </div><div class="t m1 x17 h10 y76 ff8 fs3 fc8 sc0 ls0 ws0">(pois nem a </div><div class="t m1 x18 h10 y77 ff8 fs3 fc8 sc0 ls0 ws0">caixa 20 nem </div><div class="t m1 x16 h10 y78 ff8 fs3 fc8 sc0 ls0 ws0">a da retirada 1 </div><div class="t m1 x19 h10 y79 ff8 fs3 fc8 sc0 ls0 ws0">podem estar </div><div class="t m1 x1a h10 y7a ff8 fs3 fc8 sc0 ls0 ws0">aqui) </div><div class="t m1 x1b h10 y7b ff8 fs3 fc8 sc0 ls0 ws0">1 possibilidade </div><div class="t m1 x1c h10 y7c ff8 fs3 fc8 sc0 ls0 ws0">(caixa 20) </div><div class="t m1 x1d h10 y7d ff8 fs3 fc8 sc0 ls0 ws0">87 possibilidades </div><div class="t m1 x1e h10 y7b ff8 fs3 fc8 sc0 ls0 ws0">(90 menos a </div><div class="t m1 x1d h10 y7c ff8 fs3 fc8 sc0 ls0 ws0">caixa 20 e as das </div><div class="t m1 x1f h10 y7e ff8 fs3 fc8 sc0 ls0 ws0">retiradas 1 e 2) </div><div class="t m1 xb h10 y7f ff8 fs3 fc8 sc0 ls0 ws0"> </div><div class="t m1 xb h10 y80 ff8 fs3 fc8 sc0 ls0 ws0"> <span class="blank _7"> </span>Pelo princípio fundamental da <span class="blank _1"> </span>contagem, temos: </div></div><div class="c x20 y81 w5 h12"><div class="t m5 x0 h13 y82 ffa fs7 fc3 sc0 ls5 ws6">89<span class="blank _d"> </span>88 1 87<span class="blank _1b"> </span>681384</div></div><div class="c x0 y0 w1 h0"><div class="t m5 x10 h14 y83 ffb fs7 fc3 sc0 ls0 ws7">Possibilidade<span class="blank _1"> </span>s</div></div><div class="c x21 y84 w6 h15"><div class="t m5 x0 h16 y85 ffc fs7 fc3 sc0 ls0 ws8">= ×<span class="blank _1c"> </span>×<span class="blank _1d"> </span>× =</div></div><div class="c x0 y0 w1 h0"><div class="t m1 x22 h10 y83 ff8 fs3 fc8 sc0 ls0 ws0"> </div><div class="t m1 xb hf y86 ff7 fs3 fc8 sc0 ls0 ws0">Resposta: <span class="blank _1"> </span>A<span class="blank _0"></span> </div><div class="t m1 x11 h10 y87 ff8 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 xb hf y88 ff7 fs3 fc7 sc0 ls0 ws0">1.1 Permutação simples </div><div class="t m1 xb h10 y89 ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span>Analisemos <span class="blank _16"> </span>agora <span class="blank _16"> </span>o seguinte <span class="blank _16"> </span>exemplo: <span class="blank _16"> </span>temos 5<span class="blank _1"> </span> pessoas <span class="blank _16"> </span>que de<span class="blank _1"> </span>vem se </div><div class="t m1 xb h10 y8a ff8 fs3 fc3 sc0 ls0 ws0">sentar em <span class="blank _9"> </span>uma<span class="blank _1"> </span> <span class="blank _9"> </span>f<span class="blank _1"> </span>ileira <span class="blank _9"> </span>do cinema, u<span class="blank _0"></span>ma ao<span class="blank _0"></span> <span class="blank _12"> </span>lado da <span class="blank _12"> </span>outra. <span class="blank _12"> </span>De <span class="blank _12"> </span>quantas <span class="blank _12"> </span>maneiras </div><div class="t m1 xb h10 y8b ff8 fs3 fc3 sc0 ls0 ws0">diferentes podemos sentar e<span class="blank _1"> </span>ssas pessoas? </div><div class="t m1 xb h10 y8c ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _1e"> </span>Na <span class="blank _e"> </span>primeira <span class="blank _10"> </span>cadeira, <span class="blank _e"> </span>podemos <span class="blank _e"> </span>coloca<span class="blank _1"> </span>r <span class="blank _f"> </span>qualquer <span class="blank _e"> </span>uma <span class="blank _e"> </span>da<span class="blank _1"> </span>s <span class="blank _f"> </span>5 <span class="blank _10"> </span>pessoas. <span class="blank _e"> </span>Isto <span class="blank _e"> </span>é, </div><div class="t m1 xb h10 y8d ff8 fs3 fc3 sc0 ls0 ws0">temos <span class="blank _1"> </span>5 possibilidades. <span class="blank _1"> </span>Já n<span class="blank _1"> </span>a segunda <span class="blank _1"> </span>cadeira, temos <span class="blank _1"> </span>apenas 4<span class="blank _1"> </span> possibilidades, <span class="blank _1"> </span>pois </div><div class="t m1 xb h10 y8e ff8 fs3 fc3 sc0 ls0 ws0">necessariamente <span class="blank _f"> </span>uma <span class="blank _f"> </span>pessoa<span class="blank _1"> </span> <span class="blank _f"> </span>já <span class="blank _f"> </span>estará <span class="blank _f"> </span>ocupando <span class="blank _f"> </span>a <span class="blank _f"> </span>primeira <span class="blank _f"> </span>cadeira. <span class="blank _f"> </span>Para <span class="blank _f"> </span>terceira </div><div class="t m1 xb h10 y8f ff8 fs3 fc3 sc0 ls0 ws0">cadeira <span class="blank _1"> </span>sobram 3 <span class="blank _1"> </span>possibilidades, <span class="blank _1"> </span>assim como <span class="blank _1"> </span>sobram 2<span class="blank _1"> </span> possibilidades <span class="blank _1"> </span>para <span class="blank _1"> </span>a quarta </div><div class="t m1 xb h10 y90 ff8 fs3 fc3 sc0 ls0 ws0">cadeira, e uma para a últim<span class="blank _1"> </span>a. Veja isso na tabela abaixo: <span class="blank _1f"> </span> </div><div class="t m1 x23 hf y91 ff7 fs3 fc3 sc0 ls0 ws0">Cadeira <span class="blank _20"> </span>1ª <span class="blank _21"> </span>2ª <span class="blank _21"> </span>3ª <span class="blank _21"> </span>4ª <span class="blank _21"> </span>5ª </div><div class="t m1 xb hf y92 ff7 fs3 fc3 sc0 ls0 ws9">Possibilidades</div></div><div class="c x24 y93 w7 h17"><div class="t m1 x0 hf y94 ff7 fs3 fc3 sc0 ls0 ws0"> </div></div><div class="c x0 y0 w1 h0"><div class="t m1 x25 h18 y95 ff7 fs3 fc3 sc0 ls0 ws0">de ocupação <span class="blank _22"> </span><span class="ff8 v1">5 <span class="blank _23"> </span>4 <span class="blank _23"> </span>3 <span class="blank _23"> </span>2 <span class="blank _23"> </span>1 </span></div></div><div class="t m0 x4 h5 y5 ff2 fs2 fc0 sc0 ls0 ws0">10323012795 - Rosamaria Domingues de Oliveira</div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf6" class="pf w0 h0" data-page-no="6"><div class="pc pc6 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x5 y6 w4 h6" alt src="https://files.passeidireto.com/33ce9d39-9ba4-40f4-8936-9c985004e9c6/bg6.png" alt="Pré-visualização de imagem de arquivo"><div class="c x0 y0 w1 h0"><div class="t m1 x6 h7 y7 ff3 fs3 fc2 sc0 ls0 ws1"></div></div><div class="c x7 y8 w3 h8"><div class="t m1 x0 h7 y9 ff3 fs3 fc2 sc0 ls0"></div></div><div class="c x0 y0 w1 h0"><div class="t m1 x8 h7 ya ff3 fs3 fc2 sc0 ls0 ws1"></div></div><div class="c x7 yb w3 h9"><div class="t m1 x0 h7 y9 ff3 fs3 fc2 sc0 ls0"></div></div><div class="c x0 y0 w1 h0"><div class="t m1 x9 h7 yc ff3 fs3 fc2 sc0 ls0 ws0"> !</div><div class="t m2 x7 ha yc ff4 fs4 fc3 sc0 ls0"></div><div class="t m3 xa hb yd ff4 fs5 fc2 sc0 ls0"></div><div class="t m4 xb hc ye ff5 fs6 fc3 sc0 ls0"></div><div class="t m4 xb hd yf ff3 fs6 fc4 sc0 ls0 ws2">    </div><div class="t m3 xc hb yf ff4 fs5 fc5 sc0 ls0 ws3"><span class="blank _0"></span></div><div class="t m4 xd hc yf ff5 fs6 fc4 sc0 ls1 ws4"><span class="blank _0"></span><span class="blank _0"></span><span class="ff4 ls0 ws5"><span class="blank _0"></span><span class="ff5 fc3"></span></span></div><div class="t m1 xb h10 y10 ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span> </div><div class="t m1 x11 h10 y31 ff8 fs3 fc3 sc0 ls0 ws0">Feito isso, podemo<span class="blank _1"> </span>s utiliz<span class="blank _0"></span>ar novame<span class="blank _1"> </span>nte a regra do produto pa<span class="blank _1"> </span>r<span class="blank _0"></span>a obter o </div><div class="t m1 xb h10 y32 ff8 fs3 fc3 sc0 ls0 ws0">número total de formas de sentar as pessoas: </div><div class="t m1 x26 h11 y96 ff9 fs3 fc3 sc0 ls0 ws0">Total de formas de sentar = 5 x 4 x <span class="blank _1"> </span>3 x 2 x 1 = 120 </div><div class="t m1 xb h10 y34 ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span> </div><div class="t m1 x11 h10 y35 ff8 fs3 fc3 sc0 ls0 ws0">Observe <span class="blank _10"> </span>um <span class="blank _13"> </span>detalhe <span class="blank _10"> </span>importante <span class="blank _10"> </span>neste <span class="blank _10"> </span>p<span class="blank _1"> </span>robl<span class="blank _0"></span>ema: <span class="blank _10"> </span>em <span class="blank _10"> </span>ca<span class="blank _1"> </span>da <span class="blank _e"> </span>uma <span class="blank _13"> </span>dessas <span class="blank _10"> </span>120 </div><div class="t m1 xb h10 y36 ff8 fs3 fc3 sc0 ls0 ws0">possibilidades <span class="blank _f"> </span>de <span class="blank _f"> </span>arrumação <span class="blank _f"> </span>das <span class="blank _b"> </span>pes<span class="blank _1"> </span>s<span class="blank _0"></span>oas, <span class="blank _f"> </span>as <span class="blank _b"> </span>mesma<span class="blank _1"> </span>s <span class="blank _b"> </span>5<span class="blank _1"> </span> <span class="blank _b"> </span>pessoas <span class="blank _f"> </span>estão <span class="blank _f"> </span>presentes. </div><div class="t m1 xb h10 y97 ff8 fs3 fc3 sc0 ls0 ws0">O <span class="blank _24"> </span>que <span class="blank _24"> </span>torna <span class="blank _24"> </span>diferente <span class="blank _24"> </span>uma <span class="blank _24"> </span>possibilidade <span class="blank _24"> </span>da <span class="blank _24"> </span>outra <span class="blank _8"> </span>é<span class="blank _1"> </span> <span class="blank _8"> </span>somente <span class="blank _24"> </span>a <span class="blank _24"> </span>ordem <span class="blank _24"> </span>de </div><div class="t m1 xb h10 y38 ff8 fs3 fc3 sc0 ls0 ws0">posicionamento da<span class="blank _1"> </span>s p<span class="blank _0"></span>essoas. <span class="blank _25"> </span> </div><div class="t m1 xb h10 y39 ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span>Esse tipo <span class="blank _12"> </span>de problema, <span class="blank _12"> </span>onde o <span class="blank _9"> </span>o<span class="blank _1"> </span>bjetivo <span class="blank _12"> </span>é <span class="blank _12"> </span>arrumar “n” <span class="blank _12"> </span>elementos em “<span class="blank _0"></span>n” </div><div class="t m1 xb h10 y3a ff8 fs3 fc3 sc0 ls0 ws0">posições <span class="blank _14"> </span>distintas <span class="blank _14"> </span>(no <span class="blank _14"> </span>caso, <span class="blank _14"> </span>5 <span class="blank _14"> </span>pessoas <span class="blank _15"> </span>e<span class="blank _1"> </span>m <span class="blank _15"> </span>5 <span class="blank _14"> </span>cadeiras), <span class="blank _14"> </span>e <span class="blank _14"> </span>onde <span class="blank _14"> </span>a <span class="blank _14"> </span>ordem <span class="blank _14"> </span>de </div><div class="t m1 xb h10 y3b ff8 fs3 fc3 sc0 ls0 ws0">arrumação <span class="blank _12"> </span>dos <span class="blank _9"> </span>elementos <span class="blank _9"> </span>diferencia <span class="blank _9"> </span>uma<span class="blank _1"> </span> <span class="blank _a"> </span>p<span class="blank _1"> </span>ossibilidade <span class="blank _9"> </span>da <span class="blank _9"> </span>o<span class="blank _1"> </span>utra<span class="blank _0"></span>, <span class="blank _9"> </span>é<span class="blank _1"> </span> <span class="blank _9"> </span>chamado <span class="blank _9"> </span>de </div><div class="t m1 xb h10 y55 ff8 fs3 fc3 sc0 ls0 ws0">PERMUTAÇÃO <span class="blank _1"> </span>SIMPLES. O <span class="blank _1"> </span>cálculo da pe<span class="blank _1"> </span>r<span class="blank _0"></span>mutação<span class="blank _1"> </span> simples de <span class="blank _1"> </span>n elementos <span class="blank _1"> </span>é dada </div><div class="t m1 xb h10 y56 ff8 fs3 fc3 sc0 ls0 ws0">pela fórmula abaixo: </div><div class="t m1 x27 h11 y98 ff9 fs3 fc3 sc0 ls0 ws0">P(n) = n! </div><div class="t m1 xa h11 y99 ff9 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 xb h10 y9a ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span>Nesta <span class="blank _f"> </span>fórmula, <span class="blank _f"> </span>n! <span class="blank _f"> </span>signif<span class="blank _1"> </span>ica <span class="blank _f"> </span>“n <span class="blank _f"> </span>fatorial”. <span class="blank _f"> </span>Na <span class="blank _f"> </span>matemática, <span class="blank _f"> </span>chamamos <span class="blank _f"> </span>de <span class="blank _f"> </span><span class="ff9 ws9">fatorial</span> </div><div class="t m1 xb h10 y5a ff8 fs3 fc3 sc0 ls0 ws0">de <span class="blank _a"> </span>um <span class="blank _9"> </span>número <span class="blank _a"> </span>“n” <span class="blank _a"> </span>o <span class="blank _a"> </span>produ<span class="blank _1"> </span>to <span class="blank _13"> </span>d<span class="blank _1"> </span>e <span class="blank _a"> </span>todos <span class="blank _a"> </span>os <span class="blank _a"> </span>números <span class="blank _9"> </span>inteiros <span class="blank _a"> </span>e <span class="blank _a"> </span>positivos <span class="blank _a"> </span>iguais <span class="blank _a"> </span>ou </div><div class="t m1 xb h10 y9b ff8 fs3 fc3 sc0 ls0 ws0">inferiores a n, isto é: </div><div class="t m1 xf h11 y9c ff9 fs3 fc3 sc0 ls0 ws0">n! = n x (n – 1) x (n – 2) x ... x 1 </div><div class="t m1 xa h11 y9d ff9 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 xb h10 y9e ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _1e"> </span>Exemplificando, <span class="blank _e"> </span>5! <span class="blank _f"> </span>= <span class="blank _e"> </span>5 <span class="blank _f"> </span>x <span class="blank _f"> </span>4 <span class="blank _e"> </span>x <span class="blank _f"> </span>3 <span class="blank _e"> </span>x <span class="blank _f"> </span>2 <span class="blank _e"> </span>x <span class="blank _f"> </span>1 <span class="blank _e"> </span>= <span class="blank _f"> </span>12<span class="blank _1"> </span>0. <span class="blank _f"> </span>Portanto, <span class="blank _f"> </span>se<span class="blank _1"> </span> <span class="blank _f"> </span>fossemos <span class="blank _f"> </span>aplicar </div><div class="t m1 xb h10 y9f ff8 fs3 fc3 sc0 ls0 ws0">esta fórmula na questão das cadeiras do cinem<span class="blank _1"> </span>a, teríamos: </div><div class="t m1 x28 h11 ya0 ff9 fs3 fc3 sc0 ls0 ws0">P(5) = 5 x 4 x 3 x 2 x 1 = 120 formas de posicion<span class="blank _1"> </span>ar as pessoas </div><div class="t m1 xa h11 ya1 ff9 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 xb h10 y49 ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span>Atenção <span class="blank _1"> </span>para um d<span class="blank _1"> </span>etalhe: só podemos <span class="blank _1"> </span>usar a <span class="blank _1"> </span>fórmula de <span class="blank _1"> </span>permutação simp<span class="blank _1"> </span>les<span class="blank _0"></span> </div><div class="t m1 xb h10 ya2 ff8 fs3 fc3 sc0 ls0 ws0">nos <span class="blank _1"> </span>problemas <span class="blank _1"> </span>on<span class="blank _1"> </span>de a <span class="blank _1"> </span>orde<span class="blank _1"> </span>m <span class="blank _1"> </span>de <span class="blank _1"> </span>arrumação <span class="blank _1"> </span>dos <span class="blank _1"> </span>“n” <span class="blank _1"> </span>objeto<span class="blank _1"> </span>s <span class="blank _1"> </span>torne <span class="blank _1"> </span>uma <span class="blank _1"> </span>possibilidade </div><div class="t m1 xb h10 y4b ff8 fs3 fc3 sc0 ls0 ws0">diferente <span class="blank _a"> </span>da <span class="blank _13"> </span>outra! <span class="blank _13"> </span>Vamos <span class="blank _13"> </span>n<span class="blank _1"> </span>os <span class="blank _10"> </span>d<span class="blank _1"> </span>eparar <span class="blank _13"> </span>com <span class="blank _13"> </span>vários <span class="blank _13"> </span>prob<span class="blank _1"> </span>lemas <span class="blank _13"> </span>onde <span class="blank _13"> </span>a <span class="blank _a"> </span>ordem <span class="blank _13"> </span>não </div><div class="t m1 xb h10 ya3 ff8 fs3 fc3 sc0 ls0 ws0">torna <span class="blank _15"> </span>uma <span class="blank _16"> </span>possibilidade <span class="blank _16"> </span>d<span class="blank _1"> </span>iferente <span class="blank _16"> </span>da <span class="blank _16"> </span>outra <span class="blank _16"> </span>–<span class="blank _1"> </span> <span class="blank _16"> </span>e <span class="blank _16"> </span>não<span class="blank _1"> </span> <span class="blank _16"> </span>poderemos <span class="blank _16"> </span>resolvê-los <span class="blank _16"> </span>d<span class="blank _1"> </span>e </div><div class="t m1 xb h10 ya4 ff8 fs3 fc3 sc0 ls0 ws0">maneira tão simples com<span class="blank _1"> </span>o a vista aqui. </div><div class="t m1 xb h10 ya5 ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span>Vejamos <span class="blank _16"> </span>um <span class="blank _16"> </span>outro <span class="blank _16"> </span>ex<span class="blank _0"></span>emp<span class="blank _1"> </span>lo de<span class="blank _1"> </span> permutação <span class="blank _16"> </span>simples: <span class="blank _16"> </span>quantos <span class="blank _16"> </span>anagramas </div><div class="t m1 xb h10 y4f ff8 fs3 fc3 sc0 ls0 ws0">podemos formar utilizando<span class="blank _1"> </span> todas as letras da palavra BRASIL? </div><div class="t m1 xb h10 ya6 ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span>Um <span class="blank _14"> </span>anagrama <span class="blank _14"> </span>é <span class="blank _14"> </span>um <span class="blank _15"> </span>re<span class="blank _1"> </span>arranjo <span class="blank _15"> </span>das <span class="blank _14"> </span>letras. <span class="blank _14"> </span>SILBRA, <span class="blank _14"> </span>por <span class="blank _14"> </span>exemplo, <span class="blank _14"> </span>é <span class="blank _15"> </span>um </div><div class="t m1 xb h10 y51 ff8 fs3 fc3 sc0 ls0 ws0">anagrama <span class="blank _f"> </span>d<span class="blank _1"> </span>a <span class="blank _f"> </span>palavra <span class="blank _f"> </span>BRASIL<span class="blank _1"> </span>. <span class="blank _f"> </span>Veja <span class="blank _f"> </span>que <span class="blank _e"> </span>em <span class="blank _f"> </span>BRASIL <span class="blank _e"> </span>temos <span class="blank _e"> </span>6 <span class="blank _f"> </span>letras <span class="blank _f"> </span>d<span class="blank _1"> </span>istintas <span class="blank _f"> </span>entre </div></div><div class="t m0 x4 h5 y5 ff2 fs2 fc0 sc0 ls0 ws0">10323012795 - Rosamaria Domingues de Oliveira</div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf7" class="pf w0 h0" data-page-no="7"><div class="pc pc7 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x5 y6 w2 h6" alt src="https://files.passeidireto.com/33ce9d39-9ba4-40f4-8936-9c985004e9c6/bg7.png" alt="Pré-visualização de imagem de arquivo"><div class="c x0 y0 w1 h0"><div class="t m1 x6 h7 y7 ff3 fs3 fc2 sc0 ls0 ws1"></div></div><div class="c x7 y8 w3 h8"><div class="t m1 x0 h7 y9 ff3 fs3 fc2 sc0 ls0"></div></div><div class="c x0 y0 w1 h0"><div class="t m1 x8 h7 ya ff3 fs3 fc2 sc0 ls0 ws1"></div></div><div class="c x7 yb w3 h9"><div class="t m1 x0 h7 y9 ff3 fs3 fc2 sc0 ls0"></div></div><div class="c x0 y0 w1 h0"><div class="t m1 x9 h7 yc ff3 fs3 fc2 sc0 ls0 ws0"> !</div><div class="t m2 x7 ha yc ff4 fs4 fc3 sc0 ls0"></div><div class="t m3 xa hb yd ff4 fs5 fc2 sc0 ls0"></div><div class="t m4 xb hc ye ff5 fs6 fc3 sc0 ls0"></div><div class="t m4 xb hd yf ff3 fs6 fc4 sc0 ls0 ws2">    </div><div class="t m3 xc hb yf ff4 fs5 fc5 sc0 ls0 ws3"><span class="blank _0"></span></div><div class="t m4 xd hc yf ff5 fs6 fc4 sc0 ls1 ws4"><span class="blank _0"></span><span class="blank _0"></span><span class="ff4 ls0 ws5"><span class="blank _0"></span><span class="ff5 fc3"></span></span></div><div class="t m1 xb h10 y10 ff8 fs3 fc3 sc0 ls0 ws0">si, <span class="blank _26"> </span>isto <span class="blank _26"> </span>é, <span class="blank _26"> </span>sem <span class="blank _26"> </span>repetição. <span class="blank _26"> </span>Assim, <span class="blank _26"> </span>cada <span class="blank _26"> </span>anagram<span class="blank _1"> </span>a <span class="blank _14"> </span>será <span class="blank _26"> </span>formado <span class="blank _26"> </span>po<span class="blank _1"> </span>r <span class="blank _14"> </span>6 <span class="blank _26"> </span>letras, </div><div class="t m1 xb h10 ya7 ff8 fs3 fc3 sc0 ls0 ws0">distribuídas entre 6 posições:<span class="blank _1"> </span> </div><div class="t m1 x29 hf ya8 ff7 fs3 fc3 sc0 ls0 ws0">Posição <span class="blank _27"> </span>1ª <span class="blank _28"> </span>2ª <span class="blank _28"> </span>3ª <span class="blank _28"> </span>4ª <span class="blank _28"> </span>5ª <span class="blank _29"> </span>6ª </div><div class="t m1 x2a hf ya9 ff7 fs3 fc3 sc0 ls0 ws0">Letras </div><div class="t m1 x2b h19 yaa ff7 fs3 fc3 sc0 ls0 ws0">disponíveis <span class="blank _18"> </span><span class="ff8 v1">6 <span class="blank _2a"> </span>5 <span class="blank _2a"> </span>4 <span class="blank _2a"> </span>3 <span class="blank _2a"> </span>2 <span class="blank _2b"> </span>1 </span></div><div class="t m1 xb h10 yab ff8 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 xb h10 yac ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span>Veja <span class="blank _1"> </span>que o <span class="blank _1"> </span>total <span class="blank _1"> </span>de anagramas<span class="blank _1"> </span> será <span class="blank _1"> </span>dado por <span class="blank _1"> </span>6!, <span class="blank _1"> </span>isto é,<span class="blank _1"> </span> 6 <span class="blank _1"> </span>x 5 <span class="blank _1"> </span>x 4 <span class="blank _1"> </span>x <span class="blank _1"> </span>3 x <span class="blank _1"> </span>2 <span class="blank _1"> </span>x 1 <span class="blank _1"> </span>= </div><div class="t m1 xb h10 yad ff8 fs3 fc3 sc0 ls0 ws0">720. Utilizando a fórmula: </div><div class="t m1 x2c h11 yae ff9 fs3 fc3 sc0 ls0 ws0">P(6) = 6! = 720 </div><div class="t m1 xb h10 yaf ff8 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 xb hf yb0 ff7 fs3 fc7 sc0 ls0 ws0">1.2 Permutação com repe<span class="blank _1"> </span>tição </div><div class="t m1 xb h10 yb1 ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span>Imagine <span class="blank _26"> </span>que <span class="blank _26"> </span>você <span class="blank _26"> </span>queira <span class="blank _26"> </span>calcular <span class="blank _26"> </span>o <span class="blank _26"> </span>número <span class="blank _26"> </span>de <span class="blank _26"> </span>anagramas <span class="blank _26"> </span>da <span class="blank _26"> </span>pa<span class="blank _1"> </span>lavra<span class="blank _0"></span> </div><div class="t m1 xb h10 yb2 ff8 fs3 fc3 sc0 ls0 ws0">ARARA. <span class="blank _1"> </span>A <span class="blank _1"> </span>princípio vo<span class="blank _1"> </span>cê usa<span class="blank _1"> </span>ria a <span class="blank _1"> </span>fórmu<span class="blank _1"> </span>l<span class="blank _0"></span>a <span class="blank _1"> </span>de p<span class="blank _1"> </span>ermutação <span class="blank _1"> </span>simples, co<span class="blank _1"> </span>mo f<span class="blank _1"> </span>izemos no </div><div class="t m1 xb h10 yb3 ff8 fs3 fc3 sc0 ls0 ws0">caso <span class="blank _e"> </span>de <span class="blank _e"> </span>BRASIL. <span class="blank _e"> </span>Po<span class="blank _1"> </span>r<span class="blank _0"></span>ém <span class="blank _e"> </span>ARARA <span class="blank _e"> </span>po<span class="blank _1"> </span>ssui <span class="blank _f"> </span>3 <span class="blank _e"> </span>repe<span class="blank _1"> </span>tições <span class="blank _f"> </span>da <span class="blank _e"> </span>letra<span class="blank _1"> </span> <span class="blank _f"> </span>A <span class="blank _e"> </span>e <span class="blank _e"> </span>2 <span class="blank _e"> </span>repet<span class="blank _1"> </span>ições <span class="blank _f"> </span>da </div><div class="t m1 xb h10 yb4 ff8 fs3 fc3 sc0 ls0 ws0">letra <span class="blank _e"> </span>R. <span class="blank _e"> </span>Isso <span class="blank _f"> </span>fa<span class="blank _1"> </span>z <span class="blank _f"> </span>com <span class="blank _f"> </span>que <span class="blank _e"> </span>alguns <span class="blank _e"> </span>anagramas <span class="blank _e"> </span>seja, <span class="blank _f"> </span>n<span class="blank _1"> </span>a <span class="blank _f"> </span>verdade, <span class="blank _e"> </span>repetições <span class="blank _e"> </span>uns <span class="blank _e"> </span>dos </div><div class="t m1 xb h10 yb5 ff8 fs3 fc3 sc0 ls0 ws0">outros. </div><div class="t m1 xb h10 yb6 ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span>Exemplificando, <span class="blank _f"> </span>podemos <span class="blank _b"> </span>construir <span class="blank _b"> </span>o<span class="blank _1"> </span> <span class="blank _b"> </span>anagrama <span class="blank _f"> </span>ARRAA, <span class="blank _b"> </span>onde <span class="blank _b"> </span>sim<span class="blank _1"> </span>plesmente </div><div class="t m1 xb h10 yb7 ff8 fs3 fc3 sc0 ls0 ws0">trocamos <span class="blank _10"> </span>de<span class="blank _1"> </span> <span class="blank _e"> </span>posição <span class="blank _10"> </span>o <span class="blank _10"> </span>2º<span class="blank _1"> </span> <span class="blank _e"> </span>R <span class="blank _10"> </span>com<span class="blank _1"> </span> <span class="blank _e"> </span>o <span class="blank _13"> </span>2º <span class="blank _10"> </span>A. <span class="blank _10"> </span>Este <span class="blank _10"> </span>mesmo <span class="blank _10"> </span>anagrama <span class="blank _10"> </span>p<span class="blank _1"> </span>oderia <span class="blank _10"> </span>ter <span class="blank _10"> </span>sido </div><div class="t m1 xb h10 yb8 ff8 fs3 fc3 sc0 ls0 ws0">construído <span class="blank _b"> </span>trocando <span class="blank _1"> </span>de <span class="blank _1"> </span>p<span class="blank _1"> </span>osição <span class="blank _1"> </span>o <span class="blank _1"> </span>1º <span class="blank _b"> </span>R <span class="blank _1"> </span>com<span class="blank _1"> </span> <span class="blank _1"> </span>o <span class="blank _1"> </span>2º <span class="blank _b"> </span>A, <span class="blank _1"> </span>e, <span class="blank _b"> </span>a <span class="blank _1"> </span>seguir, <span class="blank _1"> </span>colo<span class="blank _1"> </span>cando <span class="blank _1"> </span>o <span class="blank _1"> </span>1º <span class="blank _b"> </span>A <span class="blank _1"> </span>na </div><div class="t m1 xb h10 yb9 ff8 fs3 fc3 sc0 ls0 ws0">última posição. <span class="blank _16"> </span>Não podemos contar 2 vezes esses ana<span class="blank _1"> </span>gra<span class="blank _0"></span>mas, pois <span class="blank _16"> </span>eles são </div><div class="t m1 xb h10 yba ff8 fs3 fc3 sc0 ls0 ws0">idênticos. </div><div class="t m1 xb h10 ybb ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span>Por <span class="blank _15"> </span>isso, <span class="blank _15"> </span>quando <span class="blank _15"> </span>há <span class="blank _15"> </span>repetição <span class="blank _15"> </span>devemos <span class="blank _15"> </span>usar <span class="blank _15"> </span>a <span class="blank _15"> </span>fórmula <span class="blank _15"> </span>da <span class="blank _15"> </span>permutação </div><div class="t m1 xb h10 ybc ff8 fs3 fc3 sc0 ls0 ws0">simples, <span class="blank _16"> </span>porém <span class="blank _16"> </span>dividir <span class="blank _16"> </span>o re<span class="blank _1"> </span>sultado <span class="blank _16"> </span>pelo <span class="blank _16"> </span>número <span class="blank _16"> </span>de <span class="blank _16"> </span>permutações <span class="blank _16"> </span>de <span class="blank _16"> </span>cada <span class="blank _16"> </span>letra </div><div class="t m1 xb h10 ybd ff8 fs3 fc3 sc0 ls0 ws0">repetida. <span class="blank _1"> </span>Como ARARA tem <span class="blank _1"> </span>5 let<span class="blank _1"> </span>ras, sendo que o<span class="blank _1"> </span> A rep<span class="blank _1"> </span>ete-se 3 <span class="blank _1"> </span>ve<span class="blank _0"></span>zes e <span class="blank _1"> </span>o R re<span class="blank _1"> </span>pete-</div><div class="t m1 xb h10 ybe ff8 fs3 fc3 sc0 ls0 ws0">se 2 vezes, temos: </div><div class="t m6 x2d h1a ybf ffa fs8 fc3 sc0 ls0 wsa">5!</div></div><div class="c x2e yc0 w8 h1b"><div class="t m6 x0 h1a y82 ffa fs8 fc3 sc0 ls0 ws0">(5 <span class="blank _1"> </span>;<span class="blank _e"> </span> 3 <span class="blank _24"> </span> 2<span class="blank _1"> </span>)<span class="blank _2b"> </span>10</div></div><div class="c x2f yc1 w9 h1c"><div class="t m6 x0 h1a y94 ffa fs8 fc3 sc0 ls0 wsb">3!<span class="blank _19"> </span>2!</div></div><div class="c x0 y0 w1 h0"><div class="t m6 x30 h1d yc2 ffb fs8 fc3 sc0 ls0 wsc">PR e</div></div><div class="c x21 yc3 wa h9"><div class="t m6 x0 h1e y94 ffc fs8 fc3 sc0 ls0 wsd">= =</div></div><div class="c x0 y0 w1 h0"><div class="t m6 x2d h1e yc4 ffc fs8 fc3 sc0 ls0">×</div><div class="t m1 x31 h10 yc2 ff8 fs3 fc3 sc0 ls0 ws0">anagramas </div><div class="t m1 xb h10 yc5 ff8 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 xb h10 yc6 ff8 fs3 fc7 sc0 ls6 ws0"> <span class="fc3 ls0">Generalizando, <span class="blank _26"> </span>podemos <span class="blank _26"> </span>dizer <span class="blank _14"> </span>que <span class="blank _26"> </span>a <span class="blank _14"> </span>permu<span class="blank _1"> </span>tação <span class="blank _14"> </span>de <span class="blank _14"> </span>n<span class="blank _1"> </span> <span class="blank _14"> </span>elementos <span class="blank _14"> </span>c<span class="blank _1"> </span>om </span></div><div class="t m1 xb h10 yc7 ff8 fs3 fc3 sc0 ls0 ws0">repetição de m e p é dada por: </div></div><div class="c x32 yc8 wb h1b"><div class="t m1 x0 h10 y82 ffa fs3 fc3 sc0 ls0">!</div></div><div class="c x0 y0 w1 h0"><div class="t m1 x33 h10 yc9 ffa fs3 fc3 sc0 ls0 ws0">(<span class="blank _19"> </span> <span class="blank _1"> </span>;<span class="blank _e"> </span> <span class="blank _2c"> </span> <span class="blank _24"> </span> <span class="blank _2d"> </span>)</div></div><div class="c x31 yca wc h1f"><div class="t m1 x0 h10 ycb ffa fs3 fc3 sc0 ls0 wse">! !</div></div><div class="c x31 yc8 wd h1b"><div class="t m1 x0 h20 y82 ffb fs3 fc3 sc0 ls0">n</div></div><div class="c x0 y0 w1 h0"><div class="t m1 x34 h20 yc9 ffb fs3 fc3 sc0 ls0 wsf">PR<span class="blank _26"> </span>n<span class="blank _2e"> </span>m e p</div></div><div class="c x35 yca we h1f"><div class="t m1 x0 h20 ycb ffb fs3 fc3 sc0 ls0 ws10">m p</div></div><div class="c x0 y0 w1 h0"><div class="t m1 x36 h21 yc9 ffc fs3 fc3 sc0 ls0">=</div></div><div class="c x37 ycc wf h9"><div class="t m1 x0 h21 y94 ffc fs3 fc3 sc0 ls0">×</div></div><div class="c x0 y0 w1 h0"><div class="t m1 x38 h10 yc9 ff8 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 xb hf ycd ff7 fs3 fc7 sc0 ls0 ws0"> </div><div class="t m1 xb hf yce ff7 fs3 fc7 sc0 ls0 ws0">1.3 <span class="blank _1"> </span>A<span class="blank _0"></span>rranjo simples </div></div><div class="t m0 x4 h5 y5 ff2 fs2 fc0 sc0 ls0 ws0">10323012795 - Rosamaria Domingues de Oliveira</div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf8" class="pf w0 h0" data-page-no="8"><div class="pc pc8 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x5 y6 w4 h6" alt src="https://files.passeidireto.com/33ce9d39-9ba4-40f4-8936-9c985004e9c6/bg8.png" alt="Pré-visualização de imagem de arquivo"><div class="c x0 y0 w1 h0"><div class="t m1 x6 h7 y7 ff3 fs3 fc2 sc0 ls0 ws1"></div></div><div class="c x7 y8 w3 h8"><div class="t m1 x0 h7 y9 ff3 fs3 fc2 sc0 ls0"></div></div><div class="c x0 y0 w1 h0"><div class="t m1 x8 h7 ya ff3 fs3 fc2 sc0 ls0 ws1"></div></div><div class="c x7 yb w3 h9"><div class="t m1 x0 h7 y9 ff3 fs3 fc2 sc0 ls0"></div></div><div class="c x0 y0 w1 h0"><div class="t m1 x9 h7 yc ff3 fs3 fc2 sc0 ls0 ws0"> !</div><div class="t m2 x7 ha yc ff4 fs4 fc3 sc0 ls0"></div><div class="t m3 xa hb yd ff4 fs5 fc2 sc0 ls0"></div><div class="t m4 xb hc ye ff5 fs6 fc3 sc0 ls0"></div><div class="t m4 xb hd yf ff3 fs6 fc4 sc0 ls0 ws2">    </div><div class="t m3 xc hb yf ff4 fs5 fc5 sc0 ls0 ws3"><span class="blank _0"></span></div><div class="t m4 xd hc yf ff5 fs6 fc4 sc0 ls1 ws4"><span class="blank _0"></span><span class="blank _0"></span><span class="ff4 ls0 ws5"><span class="blank _0"></span><span class="ff5 fc3"></span></span></div><div class="t m1 xb h10 y10 ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span>Imagine <span class="blank _f"> </span>agora <span class="blank _f"> </span>que <span class="blank _f"> </span>quiséssemos <span class="blank _f"> </span>posicionar <span class="blank _b"> </span>aquela<span class="blank _1"> </span>s <span class="blank _b"> </span>5<span class="blank _1"> </span> <span class="blank _b"> </span>p<span class="blank _1"> </span>essoas <span class="blank _b"> </span>nas <span class="blank _f"> </span>cadeiras </div><div class="t m1 xb h10 y31 ff8 fs3 fc3 sc0 ls0 ws0">do <span class="blank _a"> </span>cinema, <span class="blank _13"> </span>ma<span class="blank _1"> </span>s <span class="blank _13"> </span>tivéssemos <span class="blank _a"> </span>apenas <span class="blank _13"> </span>3<span class="blank _1"> </span> <span class="blank _13"> </span>cadeiras <span class="blank _a"> </span>à <span class="blank _a"> </span>disposição. <span class="blank _13"> </span>De <span class="blank _a"> </span>quantas <span class="blank _13"> </span>f<span class="blank _1"> </span>ormas </div><div class="t m1 xb h10 y32 ff8 fs3 fc3 sc0 ls0 ws0">poderíamos fazer isso? </div><div class="t m1 xb h10 y33 ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span>Para <span class="blank _e"> </span>a <span class="blank _e"> </span>primeira <span class="blank _e"> </span>cadeira <span class="blank _e"> </span>temos, <span class="blank _e"> </span>novamente, <span class="blank _e"> </span>5 <span class="blank _e"> </span>pessoas <span class="blank _e"> </span>disponíveis, <span class="blank _e"> </span>isto <span class="blank _e"> </span>é, <span class="blank _e"> </span>5 </div><div class="t m1 xb h10 y34 ff8 fs3 fc3 sc0 ls0 ws0">possibilidades. <span class="blank _10"> </span>Já <span class="blank _e"> </span>para <span class="blank _e"> </span>a<span class="blank _1"> </span> <span class="blank _f"> </span>se<span class="blank _1"> </span>gunda <span class="blank _e"> </span>cadeira, <span class="blank _e"> </span>restam<span class="blank _1"> </span>-nos <span class="blank _f"> </span>4<span class="blank _1"> </span> <span class="blank _f"> </span>p<span class="blank _1"> </span>ossibilidades, <span class="blank _e"> </span>dado <span class="blank _e"> </span>que </div><div class="t m1 xb h10 y35 ff8 fs3 fc3 sc0 ls0 ws0">uma <span class="blank _9"> </span>já <span class="blank _9"> </span>foi <span class="blank _9"> </span>utilizada <span class="blank _9"> </span>na <span class="blank _9"> </span>primeira <span class="blank _9"> </span>cadeira. <span class="blank _9"> </span>Por <span class="blank _9"> </span>fim, <span class="blank _9"> </span>na <span class="blank _9"> </span>terceira <span class="blank _9"> </span>cadeira <span class="blank _9"> </span>pode<span class="blank _1"> </span>remos<span class="blank _0"></span> </div><div class="t m1 xb h10 y36 ff8 fs3 fc3 sc0 ls0 ws0">colocar <span class="blank _1"> </span>qualquer <span class="blank _1"> </span>das <span class="blank _1"> </span>3 <span class="blank _1"> </span>pessoas <span class="blank _1"> </span>restantes. <span class="blank _1"> </span>Veja <span class="blank _1"> </span>que <span class="blank _1"> </span>se<span class="blank _0"></span>mpre <span class="blank _1"> </span>sobrarão <span class="blank _1"> </span>duas <span class="blank _1"> </span>pessoas </div><div class="t m1 xb h10 y37 ff8 fs3 fc3 sc0 ls0 ws0">em pé<span class="blank _1"> </span>, afinal temos <span class="blank _1"> </span>apenas 3 ca<span class="blank _1"> </span>deiras. A quantidade<span class="blank _1"> </span> de formas d<span class="blank _1"> </span>e posicionar es<span class="blank _1"> </span>sas<span class="blank _0"></span> </div><div class="t m1 xb h10 y38 ff8 fs3 fc3 sc0 ls0 ws0">pessoas sentadas é dada pe<span class="blank _1"> </span>la multiplicação abaixo:<span class="blank _0"></span> </div><div class="t m1 x28 h11 ycf ff9 fs3 fc3 sc0 ls0 ws0">Formas de organi<span class="blank _1"> </span>z<span class="blank _0"></span>ar 5 pessoas em 3 cadeiras = 5 x 4<span class="blank _1"> </span> x 3 = 60<span class="blank _0"></span> </div><div class="t m1 xb h10 y53 ff8 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 xb h10 y54 ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span>Um <span class="blank _a"> </span>ca<span class="blank _1"> </span>s<span class="blank _0"></span>o <span class="blank _a"> </span>com<span class="blank _1"> </span>o <span class="blank _a"> </span>esse, <span class="blank _a"> </span>onde <span class="blank _a"> </span>pretendemo<span class="blank _1"> </span>s<span class="blank _0"></span> <span class="blank _a"> </span>posiciona<span class="blank _1"> </span>r <span class="blank _a"> </span>“n” <span class="blank _a"> </span>elementos <span class="blank _a"> </span>em <span class="blank _9"> </span>“m” </div><div class="t m1 xb h10 y55 ff8 fs3 fc3 sc0 ls0 ws0">posições <span class="blank _11"> </span>(m <span class="blank _26"> </span>m<span class="blank _1"> </span>enor <span class="blank _26"> </span>que <span class="blank _11"> </span>n), <span class="blank _11"> </span>e <span class="blank _11"> </span>onde <span class="blank _11"> </span>a <span class="blank _11"> </span>ordem <span class="blank _11"> </span>dos <span class="blank _11"> </span>elementos <span class="blank _26"> </span>dife<span class="blank _1"> </span>rencia <span class="blank _26"> </span>uma </div><div class="t m1 xb h10 y3d ff8 fs3 fc3 sc0 ls0 ws0">possibilidade <span class="blank _a"> </span>da <span class="blank _a"> </span>outra, <span class="blank _13"> </span>é<span class="blank _1"> </span> <span class="blank _13"> </span>cha<span class="blank _1"> </span>mada <span class="blank _13"> </span>de <span class="blank _a"> </span>ARRANJO <span class="blank _a"> </span>SIMPLES. <span class="blank _a"> </span>Sua <span class="blank _13"> </span>f<span class="blank _1"> </span>órmula <span class="blank _a"> </span>é <span class="blank _13"> </span>dada </div><div class="t m1 xb h10 y57 ff8 fs3 fc3 sc0 ls0 ws0">abaixo: </div></div><div class="c x39 yd0 wf h22"><div class="t m7 x0 h23 yd1 ffa fs9 fc3 sc0 ls0">!</div></div><div class="c x0 y0 w1 h0"><div class="t m7 x2c h23 yd2 ffa fs9 fc3 sc0 ls0 ws11">( ,<span class="blank _2e"> </span>)</div></div><div class="c x3a yd3 w10 h24"><div class="t m7 x0 h23 yd1 ffa fs9 fc3 sc0 ls0 ws12">(<span class="blank _2f"> </span>) !</div></div><div class="c x0 y0 w1 h0"><div class="t m7 x3b h25 yd4 ffb fs9 fc3 sc0 ls0">n</div><div class="t m7 x3c h25 yd5 ffb fs9 fc3 sc0 ls0 ws13">A n<span class="blank _11"> </span>m</div></div><div class="c x1c yd3 w11 h24"><div class="t m7 x0 h25 yd1 ffb fs9 fc3 sc0 ls0 ws14">n m</div></div><div class="c x0 y0 w1 h0"><div class="t m7 x3d h26 yd2 ffc fs9 fc3 sc0 ls7">=<span class="ls0 v2">−</span></div><div class="t m1 x3e h10 yd6 ff8 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 xa h10 yd7 ff8 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 xb h10 yd8 ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span>Exemplificando, em nosso e<span class="blank _1"> </span>xemplo temos n = 5 e m = 3. Portanto, teríamos: </div><div class="t m8 x3f h27 y23 ffa fsa fc3 sc0 ls0">!</div><div class="t m8 x40 h27 yd9 ffa fsa fc3 sc0 ls0 ws15">( ,<span class="blank _c"> </span>)<span class="blank _30"> </span><span class="ws16 v3">(<span class="blank _31"> </span>) !</span></div></div><div class="c x41 yda w12 h1f"><div class="t m8 x0 h27 ycb ffa fsa fc3 sc0 ls0 ws17">5!<span class="blank _32"> </span>5!<span class="blank _33"> </span>5<span class="blank _2c"> </span>4<span class="blank _34"> </span>3<span class="blank _34"> </span>2<span class="blank _35"> </span>1</div></div><div class="c x0 y0 w1 h0"><div class="t m8 x40 h27 ydb ffa fsa fc3 sc0 ls0 ws18">(5<span class="blank _0"></span>, 3<span class="blank _0"></span>)<span class="blank _33"> </span><span class="ws19 v3">(5<span class="blank _d"> </span>3<span class="blank _0"></span>) !<span class="blank _33"> </span>2 !<span class="blank _36"> </span>2<span class="blank _35"> </span>1</span></div><div class="t m8 x40 h27 ydc ffa fsa fc3 sc0 ls0 ws18">(5<span class="blank _0"></span>, 3<span class="blank _0"></span>)<span class="blank _2e"> </span>5<span class="blank _34"> </span>4<span class="blank _34"> </span>3<span class="blank _2e"> </span>60</div><div class="t m8 x21 h28 ydd ffb fsa fc3 sc0 ls0">n</div><div class="t m8 x18 h28 yde ffb fsa fc3 sc0 ls0 ws1a">A n<span class="blank _14"> </span>m<span class="blank _37"> </span><span class="ws1b v3">n m</span></div><div class="t m8 x18 h28 ydb ffb fsa fc3 sc0 ls0">A</div><div class="t m8 x18 h28 ydf ffb fsa fc3 sc0 ls0">A</div><div class="t m8 x42 h29 ye0 ffc fsa fc3 sc0 ls8">=<span class="ls0 v3">−</span></div></div><div class="c x43 ye1 w13 h9"><div class="t m8 x0 h29 y94 ffc fsa fc3 sc0 ls0 ws1c">× ×<span class="blank _35"> </span>× ×</div></div><div class="c x0 y0 w1 h0"><div class="t m8 x34 h29 ydb ffc fsa fc3 sc0 ls0 ws1d">=<span class="blank _38"> </span>= =</div><div class="t m8 x41 h29 ye2 ffc fsa fc3 sc0 ls0 ws1e">− ×</div><div class="t m8 x34 h29 ydc ffc fsa fc3 sc0 ls0 ws1c">=<span class="blank _2c"> </span>× ×<span class="blank _d"> </span>=</div><div class="t m1 x1d h10 ye3 ff8 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 xa h10 ye4 ff8 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 xb h10 ye5 ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span>Lembre-se: <span class="blank _24"> </span>estamos <span class="blank _8"> </span>falando <span class="blank _8"> </span>no<span class="blank _1"> </span>vamente<span class="blank _0"></span> <span class="blank _8"> </span>de <span class="blank _24"> </span>casos <span class="blank _8"> </span>onde <span class="blank _24"> </span>a <span class="blank _8"> </span>ordem <span class="blank _8"> </span>do<span class="blank _1"> </span>s </div><div class="t m1 xb h10 ye6 ff8 fs3 fc3 sc0 ls0 ws0">elementos <span class="blank _f"> </span>im<span class="blank _1"> </span>porta, <span class="blank _f"> </span>isto <span class="blank _f"> </span>é, <span class="blank _e"> </span>a <span class="blank _f"> </span>o<span class="blank _1"> </span>rdem <span class="blank _f"> </span>dos <span class="blank _f"> </span>elemento<span class="blank _1"> </span>s <span class="blank _f"> </span>diferencia <span class="blank _f"> </span>uma <span class="blank _e"> </span>possibilidade <span class="blank _e"> </span>de </div><div class="t m1 xb h10 ye7 ff8 fs3 fc3 sc0 ls0 ws0">outra. <span class="blank _1"> </span>Imagine <span class="blank _1"> </span>que as 5<span class="blank _1"> </span> pe<span class="blank _1"> </span>ssoas sejam: <span class="blank _1"> </span>Ana, Be<span class="blank _1"> </span>to, Carlos, <span class="blank _1"> </span>Daniela e<span class="blank _1"> </span> Eduardo. <span class="blank _1"> </span>Uma </div><div class="t m1 xb h10 ye8 ff8 fs3 fc3 sc0 ls0 ws0">forma de posicionar essas p<span class="blank _1"> </span>essoas em 3 cadeiras seria: </div><div class="t m1 x44 hf ye9 ff7 fs3 fc3 sc0 ls0 ws0">Cadeira <span class="blank _20"> </span>1ª <span class="blank _21"> </span>2ª <span class="blank _21"> </span>3ª </div><div class="t m1 x45 hf yea ff7 fs3 fc3 sc0 ls0 ws0">Ocupante <span class="blank _22"> </span><span class="ff8">Beto <span class="blank _39"> </span>Daniela <span class="blank _3a"> </span>Eduardo </span></div><div class="t m1 x11 h10 yeb ff8 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 xb h10 yec ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span>Neste <span class="blank _9"> </span>ca<span class="blank _1"> </span>so, <span class="blank _9"> </span>Ana <span class="blank _9"> </span>e<span class="blank _1"> </span> <span class="blank _9"> </span>Carlos <span class="blank _9"> </span>estã<span class="blank _1"> </span>o <span class="blank _9"> </span>de <span class="blank _9"> </span>fo<span class="blank _1"> </span>ra. <span class="blank _9"> </span>Outra <span class="blank _9"> </span>forma <span class="blank _12"> </span>de <span class="blank _9"> </span>posicioname<span class="blank _1"> </span>nt<span class="blank _0"></span>o </div><div class="t m1 xb h10 yed ff8 fs3 fc3 sc0 ls0 ws0">seria: </div></div><div class="t m0 x4 h5 y5 ff2 fs2 fc0 sc0 ls0 ws0">10323012795 - Rosamaria Domingues de Oliveira</div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf9" class="pf w0 h0" data-page-no="9"><div class="pc pc9 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x5 y6 w4 h6" alt src="https://files.passeidireto.com/33ce9d39-9ba4-40f4-8936-9c985004e9c6/bg9.png" alt="Pré-visualização de imagem de arquivo"><div class="c x0 y0 w1 h0"><div class="t m1 x6 h7 y7 ff3 fs3 fc2 sc0 ls0 ws1"></div></div><div class="c x7 y8 w3 h8"><div class="t m1 x0 h7 y9 ff3 fs3 fc2 sc0 ls0"></div></div><div class="c x0 y0 w1 h0"><div class="t m1 x8 h7 ya ff3 fs3 fc2 sc0 ls0 ws1"></div></div><div class="c x7 yb w3 h9"><div class="t m1 x0 h7 y9 ff3 fs3 fc2 sc0 ls0"></div></div><div class="c x0 y0 w1 h0"><div class="t m1 x9 h7 yc ff3 fs3 fc2 sc0 ls0 ws0"> !</div><div class="t m2 x7 ha yc ff4 fs4 fc3 sc0 ls0"></div><div class="t m3 xa hb yd ff4 fs5 fc2 sc0 ls0"></div><div class="t m4 xb hc ye ff5 fs6 fc3 sc0 ls0"></div><div class="t m4 xb hd yf ff3 fs6 fc4 sc0 ls0 ws2">    </div><div class="t m3 xc hb yf ff4 fs5 fc5 sc0 ls0 ws3"><span class="blank _0"></span></div><div class="t m4 xd hc yf ff5 fs6 fc4 sc0 ls1 ws4"><span class="blank _0"></span><span class="blank _0"></span><span class="ff4 ls0 ws5"><span class="blank _0"></span><span class="ff5 fc3"></span></span></div><div class="t m1 x44 hf yee ff7 fs3 fc3 sc0 ls0 ws0">Cadeira <span class="blank _20"> </span>1ª <span class="blank _21"> </span>2ª <span class="blank _21"> </span>3ª </div><div class="t m1 x45 hf yef ff7 fs3 fc3 sc0 ls0 ws0">Ocupante <span class="blank _7"> </span><span class="ff8">Daniela <span class="blank _39"> </span>B<span class="blank _1"> </span>eto <span class="blank _36"> </span>Eduardo </span></div><div class="t m1 xb h10 yf0 ff8 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 xb h10 yf1 ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span>Veja <span class="blank _1"> </span>que, <span class="blank _1"> </span>novamente, An<span class="blank _1"> </span>a e <span class="blank _1"> </span>Carlos <span class="blank _1"> </span>estão <span class="blank _1"> </span>de fo<span class="blank _1"> </span>ra. E <span class="blank _1"> </span>Eduardo <span class="blank _1"> </span>está no<span class="blank _1"> </span> mesmo </div><div class="t m1 xb h10 yf2 ff8 fs3 fc3 sc0 ls0 ws0">lugar. <span class="blank _f"> </span>A<span class="blank _1"> </span> <span class="blank _f"> </span>única<span class="blank _1"> </span> <span class="blank _f"> </span>mudança <span class="blank _e"> </span>foi <span class="blank _e"> </span>a <span class="blank _e"> </span>inversão <span class="blank _e"> </span>de <span class="blank _e"> </span>posições <span class="blank _e"> </span>entre <span class="blank _e"> </span>Beto <span class="blank _e"> </span>e <span class="blank _f"> </span>Dan<span class="blank _1"> </span>iela. <span class="blank _f"> </span>Ou <span class="blank _e"> </span>seja, </div><div class="t m1 xb h10 yf3 ff8 fs3 fc3 sc0 ls0 ws0">uma <span class="blank _a"> </span>simples <span class="blank _13"> </span>alteração <span class="blank _a"> </span>na <span class="blank _13"> </span>ordem <span class="blank _a"> </span>dos <span class="blank _13"> </span>elemen<span class="blank _1"> </span>tos <span class="blank _13"> </span>gera <span class="blank _13"> </span>um<span class="blank _1"> </span>a <span class="blank _13"> </span>nova <span class="blank _13"> </span>possib<span class="blank _1"> </span>ilidade <span class="blank _13"> </span>de </div><div class="t m1 xb h10 yf4 ff8 fs3 fc3 sc0 ls0 ws0">posicionamento. <span class="blank _f"> </span>É <span class="blank _f"> </span>isso <span class="blank _b"> </span>que <span class="blank _f"> </span>quero <span class="blank _f"> </span>dizer <span class="blank _f"> </span>quando <span class="blank _f"> </span>a<span class="blank _0"></span>firmo<span class="blank _1"> </span> <span class="blank _b"> </span>que <span class="blank _f"> </span>“a <span class="blank _f"> </span>ordem <span class="blank _f"> </span>i<span class="blank _0"></span>mpo<span class="blank _1"> </span>rt<span class="blank _0"></span>a” <span class="blank _f"> </span>para </div><div class="t m1 xb h10 yf5 ff8 fs3 fc3 sc0 ls0 ws0">os casos de Permutação e Arranjo. </div><div class="t m1 xb h10 yf6 ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span>Note <span class="blank _14"> </span>a<span class="blank _1"> </span>inda <span class="blank _14"> </span>que <span class="blank _14"> </span>podem<span class="blank _1"> </span>os <span class="blank _15"> </span>u<span class="blank _1"> </span>sar <span class="blank _14"> </span>a <span class="blank _14"> </span>fórmula <span class="blank _14"> </span>d<span class="blank _1"> </span>e <span class="blank _14"> </span>Arranjo <span class="blank _14"> </span>pa<span class="blank _1"> </span>ra <span class="blank _14"> </span>resolver <span class="blank _14"> </span>um </div><div class="t m1 xb h10 yf7 ff8 fs3 fc3 sc0 ls0 ws0">problema <span class="blank _26"> </span>de <span class="blank _26"> </span>Permutação <span class="blank _26"> </span>simples. <span class="blank _26"> </span>Isto <span class="blank _26"> </span>porque <span class="blank _26"> </span>a <span class="blank _26"> </span>permutação <span class="blank _26"> </span>também <span class="blank _26"> </span>é <span class="blank _26"> </span>uma </div><div class="t m1 xb h10 yb0 ff8 fs3 fc3 sc0 ls0 ws0">ordenação <span class="blank _b"> </span>de <span class="blank _b"> </span>“n” <span class="blank _1"> </span>elemen<span class="blank _1"> </span>tos <span class="blank _1"> </span>em <span class="blank _b"> </span>“m” <span class="blank _1"> </span>posições, <span class="blank _b"> </span>po<span class="blank _1"> </span>rém<span class="blank _0"></span> <span class="blank _b"> </span>nos <span class="blank _1"> </span>ca<span class="blank _1"> </span>sos <span class="blank _1"> </span>de <span class="blank _b"> </span>permutação <span class="blank _1"> </span>n <span class="blank _b"> </span>= </div><div class="t m1 xb h10 yf8 ff8 fs3 fc3 sc0 ls0 ws0">m. <span class="blank _12"> </span>Sabendo <span class="blank _12"> </span>que <span class="blank _9"> </span>0! <span class="blank _12"> </span>é, <span class="blank _12"> </span>por <span class="blank _9"> </span>def<span class="blank _1"> </span>inição, <span class="blank _9"> </span>igual <span class="blank _12"> </span>a <span class="blank _9"> </span>1,<span class="blank _1"> </span> <span class="blank _9"> </span>podemos calcul<span class="blank _0"></span>ar <span class="blank _12"> </span>o <span class="blank _9"> </span>nú<span class="blank _1"> </span>mero <span class="blank _9"> </span>de </div><div class="t m1 xb h10 yf9 ff8 fs3 fc3 sc0 ls0 ws0">permutações de 5 pe<span class="blank _1"> </span>ssoas em 5 cadeiras de cinema com a fórmula de arranjo: </div><div class="t m1 xb h10 yfa ff8 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m8 x3f h27 yfb ffa fsa fc3 sc0 ls0">!</div><div class="t m8 x40 h27 yfc ffa fsa fc3 sc0 ls0 ws15">( ,<span class="blank _c"> </span>)<span class="blank _30"> </span><span class="ws16 v3">(<span class="blank _31"> </span>) !</span></div></div><div class="c x41 yfd w14 h1f"><div class="t m8 x0 h27 ycb ffa fsa fc3 sc0 ls0 ws1f">5!<span class="blank _32"> </span>5!<span class="blank _33"> </span>5 4 3 2<span class="blank _35"> </span>1</div></div><div class="c x0 y0 w1 h0"><div class="t m8 x40 h27 yfe ffa fsa fc3 sc0 ls0 ws18">(5<span class="blank _0"></span>, 5)<span class="blank _33"> </span><span class="ws19 v3">(5<span class="blank _d"> </span>5) !<span class="blank _3b"> </span>0 !<span class="blank _3c"> </span>1</span></div><div class="t m8 x40 h27 yff ffa fsa fc3 sc0 ls0 ws18">(5<span class="blank _0"></span>, 5)<span class="blank _3d"> </span>120</div><div class="t m8 x21 h28 y100 ffb fsa fc3 sc0 ls0">n</div><div class="t m8 x18 h28 y101 ffb fsa fc3 sc0 ls0 ws1a">A n<span class="blank _14"> </span>m<span class="blank _37"> </span><span class="ws1b v3">n m</span></div><div class="t m8 x18 h28 yfe ffb fsa fc3 sc0 ls0">A</div><div class="t m8 x18 h28 y102 ffb fsa fc3 sc0 ls0">A</div><div class="t m8 x42 h29 y103 ffc fsa fc3 sc0 ls8">=<span class="ls0 v3">−</span></div></div><div class="c x43 y104 w15 h9"><div class="t m8 x0 h29 y94 ffc fsa fc3 sc0 ls0 ws20">× ×<span class="blank _35"> </span>× ×</div></div><div class="c x0 y0 w1 h0"><div class="t m8 x34 h29 yfe ffc fsa fc3 sc0 ls0 ws21">=<span class="blank _38"> </span>= =</div><div class="t m8 x41 h29 y105 ffc fsa fc3 sc0 ls0">−</div><div class="t m8 x34 h29 yff ffc fsa fc3 sc0 ls0">=</div><div class="t m1 x1d h10 y106 ff8 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 xb h10 y107 ff8 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 xb h10 ye0 ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span>Antes de avançarmos, traba<span class="blank _1"> </span>lhe esta questão: </div><div class="t m1 xb hf y108 ff7 fs3 fc8 sc0 ls0 ws0"> </div><div class="t m1 xb hf y109 ff7 fs3 fc8 sc0 ls0 ws0">2. <span class="blank _13"> </span>E<span class="blank _1"> </span>SA<span class="blank _0"></span>F <span class="blank _13"> </span>– <span class="blank _a"> </span>CGU <span class="blank _13"> </span>– <span class="blank _13"> </span>2<span class="blank _1"> </span>008) <span class="blank _13"> </span><span class="ff8">Ágata<span class="blank _1"> </span> <span class="blank _13"> </span>é <span class="blank _13"> </span>decoradora <span class="blank _a"> </span>e <span class="blank _13"> </span>precisa <span class="blank _a"> </span>atender <span class="blank _13"> </span>o <span class="blank _13"> </span>pe<span class="blank _1"> </span>dido <span class="blank _13"> </span>de <span class="blank _13"> </span>um </span></div><div class="t m1 xb h10 y10a ff8 fs3 fc8 sc0 ls0 ws0">excêntrico clien<span class="blank _1"> </span>te. Ele - o <span class="blank _1"> </span>cliente - exige que<span class="blank _1"> </span> uma das <span class="blank _1"> </span>paredes do quarto d<span class="blank _1"> </span>e sua f<span class="blank _1"> </span>il<span class="blank _0"></span>ha </div><div class="t m1 xb h10 y10b ff8 fs3 fc8 sc0 ls0 ws0">seja dividida em<span class="blank _1"> </span> uma sequência de 5 listras horizontais pinta<span class="blank _1"> </span>das de cores diferentes, </div><div class="t m1 xb h10 y10c ff8 fs3 fc8 sc0 ls0 ws0">ou <span class="blank _8"> </span>seja, <span class="blank _8"> </span>uma <span class="blank _8"> </span>de <span class="blank _8"> </span>cada <span class="blank _8"> </span>cor. <span class="blank _8"> </span>Sabendo-se <span class="blank _8"> </span>que <span class="blank _8"> </span>Ágata <span class="blank _8"> </span>possui <span class="blank _8"> </span>apenas <span class="blank _8"> </span>8 <span class="blank _8"> </span>cores </div><div class="t m1 xb h10 y10d ff8 fs3 fc8 sc0 ls0 ws0">disponíveis, <span class="blank _b"> </span>então <span class="blank _b"> </span>o<span class="blank _1"> </span> <span class="blank _1"> </span>número <span class="blank _b"> </span>de <span class="blank _f"> </span>di<span class="blank _0"></span>ferentes <span class="blank _b"> </span>mane<span class="blank _1"> </span>iras <span class="blank _1"> </span>que <span class="blank _b"> </span>a <span class="blank _f"> </span>parede <span class="blank _1"> </span>pode <span class="blank _b"> </span>se<span class="blank _1"> </span>r <span class="blank _1"> </span>pintada </div><div class="t m1 xb h10 y10e ff8 fs3 fc8 sc0 ls0 ws0">é igual a: </div><div class="t m1 xb h10 y10f ff8 fs3 fc8 sc0 ls0 ws0">a) 56 </div><div class="t m1 xb h10 y110 ff8 fs3 fc8 sc0 ls0 ws0">b) 5760 </div><div class="t m1 xb h10 y111 ff8 fs3 fc8 sc0 ls0 ws0">c) 6720 </div><div class="t m1 xb h10 y112 ff8 fs3 fc8 sc0 ls0 ws0">d) 3600 </div><div class="t m1 xb h10 y113 ff8 fs3 fc8 sc0 ls0 ws0">e) 4320 </div><div class="t m1 xb hf y114 ff7 fs3 fc8 sc0 ls0 ws0">RESOLUÇÃO: </div></div><div class="t m0 x4 h5 y5 ff2 fs2 fc0 sc0 ls0 ws0">10323012795 - Rosamaria Domingues de Oliveira</div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pfa" class="pf w0 h0" data-page-no="a"><div class="pc pca w0 h0"><img fetchpriority="low" loading="lazy" class="bi x5 y6 w4 h6" alt src="https://files.passeidireto.com/33ce9d39-9ba4-40f4-8936-9c985004e9c6/bga.png" alt="Pré-visualização de imagem de arquivo"><div class="c x0 y0 w1 h0"><div class="t m1 x6 h7 y7 ff3 fs3 fc2 sc0 ls0 ws1"></div></div><div class="c x7 y8 w3 h8"><div class="t m1 x0 h7 y9 ff3 fs3 fc2 sc0 ls0"></div></div><div class="c x0 y0 w1 h0"><div class="t m1 x8 h7 ya ff3 fs3 fc2 sc0 ls0 ws1"></div></div><div class="c x7 yb w3 h9"><div class="t m1 x0 h7 y9 ff3 fs3 fc2 sc0 ls0"></div></div><div class="c x0 y0 w1 h0"><div class="t m1 x9 h7 yc ff3 fs3 fc2 sc0 ls0 ws0"> !</div><div class="t m2 x7 ha yc ff4 fs4 fc3 sc0 ls0"></div><div class="t m3 xa hb yd ff4 fs5 fc2 sc0 ls0"></div><div class="t m4 xb hc ye ff5 fs6 fc3 sc0 ls0"></div><div class="t m4 xb hd yf ff3 fs6 fc4 sc0 ls0 ws2">    </div><div class="t m3 xc hb yf ff4 fs5 fc5 sc0 ls0 ws3"><span class="blank _0"></span></div><div class="t m4 xd hc yf ff5 fs6 fc4 sc0 ls1 ws4"><span class="blank _0"></span><span class="blank _0"></span><span class="ff4 ls0 ws5"><span class="blank _0"></span><span class="ff5 fc3"></span></span></div><div class="t m1 xb hf y10 ff7 fs3 fc8 sc0 ls9 ws0"> <span class="ff8 ls0">Se temos 8 cores disponíveis, a primeira listra poderá ser pintada<span class="blank _1"> </span> d<span class="blank _0"></span>e 8 </span></div><div class="t m1 xb h10 y31 ff8 fs3 fc8 sc0 ls0 ws0">maneiras distintas.<span class="blank _1"> </span> A<span class="blank _0"></span> segunda<span class="blank _1"> </span> listra poderá ser pintada com uma das <span class="blank _16"> </span>7 cores </div><div class="t m1 xb h10 y32 ff8 fs3 fc8 sc0 ls0 ws0">restantes, já que<span class="blank _1"> </span> uma cor já foi utilizada na primeira listra. A<span class="blank _1"> </span> terceira listra poderá ser </div><div class="t m1 xb h10 y33 ff8 fs3 fc8 sc0 ls0 ws0">pintada <span class="blank _b"> </span>de <span class="blank _1"> </span>6 <span class="blank _b"> </span>maneiras <span class="blank _1"> </span>diferen<span class="blank _1"> </span>tes, <span class="blank _1"> </span>a <span class="blank _1"> </span>quarta <span class="blank _1"> </span>de <span class="blank _b"> </span>5 <span class="blank _1"> </span>ma<span class="blank _1"> </span>neiras, <span class="blank _1"> </span>e <span class="blank _1"> </span>a <span class="blank _b"> </span>quinta <span class="blank _1"> </span>de<span class="blank _1"> </span> 4<span class="blank _1"> </span> <span class="blank _1"> </span>maneiras </div><div class="t m1 xb h10 y34 ff8 fs3 fc8 sc0 ls0 ws0">distintas. O que disse aqui está<span class="blank _1"> </span> refletido no esq<span class="blank _0"></span>uem<span class="blank _1"> </span>a abaix<span class="blank _0"></span>o: </div><div class="t m1 x23 he y115 ff6 fs3 fc8 sc0 ls0 ws0">Listra 1 <span class="blank _29"> </span>Listra 2 <span class="blank _3e"> </span>Listra 3 <span class="blank _3e"> </span>Li<span class="blank _1"> </span>stra 4 <span class="blank _3e"> </span>Listra 5 </div><div class="t m1 x29 h10 y116 ff8 fs3 fc8 sc0 ls0 ws0">8 opções <span class="blank _38"> </span>7 opções <span class="blank _3f"> </span>6 opções <span class="blank _38"> </span>5 opções <span class="blank _3f"> </span>4 op<span class="blank _1"> </span>ções </div><div class="t m1 xb h10 y117 ff8 fs3 fc8 sc0 ls0 ws0"> </div><div class="t m1 x11 h10 y118 ff8 fs3 fc8 sc0 ls0 ws0">Pelo <span class="blank _f"> </span>princípio <span class="blank _b"> </span>f<span class="blank _1"> </span>undamental <span class="blank _f"> </span>da <span class="blank _f"> </span>contagem, <span class="blank _b"> </span>o <span class="blank _f"> </span>número <span class="blank _f"> </span>de <span class="blank _b"> </span>ma<span class="blank _1"> </span>neiras <span class="blank _b"> </span>distintas <span class="blank _f"> </span>de </div><div class="t m1 xb h10 y119 ff8 fs3 fc8 sc0 ls0 ws0">pintar a parede é de: </div><div class="t m1 x46 h10 y11a ff8 fs3 fc8 sc0 ls0 ws0">8 x 7 x 6 x 5 x 4 = 6720 </div><div class="t m1 x11 h10 y11b ff8 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 x11 h10 y11c ff8 fs3 fc3 sc0 ls0 ws0">Já <span class="blank _10"> </span>ch<span class="blank _1"> </span>egamos <span class="blank _10"> </span>ao <span class="blank _13"> </span>gabarito. <span class="blank _10"> </span>Mas <span class="blank _13"> </span>repare <span class="blank _13"> </span>que <span class="blank _10"> </span>se <span class="blank _13"> </span>trata <span class="blank _10"> </span>d<span class="blank _1"> </span>e <span class="blank _e"> </span>u<span class="blank _1"> </span>m <span class="blank _10"> </span>arranjo <span class="blank _10"> </span>sim<span class="blank _1"> </span>ples,<span class="blank _0"></span> </div><div class="t m1 xb h10 y11d ff8 fs3 fc3 sc0 ls0 ws0">afinal <span class="blank _f"> </span>queremos <span class="blank _f"> </span>dispor <span class="blank _f"> </span>8 <span class="blank _f"> </span>elementos <span class="blank _f"> </span>(cores) <span class="blank _f"> </span>em <span class="blank _f"> </span>5 <span class="blank _f"> </span>posições <span class="blank _f"> </span>(listras), <span class="blank _f"> </span>e <span class="blank _f"> </span>a <span class="blank _f"> </span>ordem <span class="blank _f"> </span>das<span class="blank _0"></span> </div><div class="t m1 xb h10 y11e ff8 fs3 fc3 sc0 ls0 ws0">cores <span class="blank _f"> </span>torna <span class="blank _f"> </span>uma <span class="blank _f"> </span>disposição <span class="blank _f"> </span>diferente <span class="blank _f"> </span>da <span class="blank _f"> </span>outra. <span class="blank _f"> </span>Isto <span class="blank _f"> </span>é, <span class="blank _b"> </span>p<span class="blank _1"> </span>intar <span class="blank _f"> </span>uma <span class="blank _f"> </span>listr<span class="blank _0"></span>a <span class="blank _f"> </span>de <span class="blank _f"> </span>Azul <span class="blank _f"> </span>e <span class="blank _f"> </span>a </div><div class="t m1 xb h10 y11f ff8 fs3 fc3 sc0 ls0 ws0">seguinte <span class="blank _e"> </span>de <span class="blank _f"> </span>Verde <span class="blank _e"> </span>é <span class="blank _f"> </span>dif<span class="blank _1"> </span>erente <span class="blank _f"> </span>de <span class="blank _f"> </span>p<span class="blank _1"> </span>intar <span class="blank _f"> </span>a <span class="blank _f"> </span>prime<span class="blank _1"> </span>ira <span class="blank _f"> </span>de <span class="blank _f"> </span>Verde <span class="blank _e"> </span>e <span class="blank _f"> </span>a<span class="blank _1"> </span> <span class="blank _f"> </span>segunda <span class="blank _f"> </span>de <span class="blank _e"> </span>Azul. </div><div class="t m1 xb h10 y120 ff8 fs3 fc3 sc0 ls0 ws0">Utilizando a fórmula de arranjo<span class="blank _1"> </span>, teríamos:<span class="blank _0"></span> </div></div><div class="c x39 y121 wf h24"><div class="t m7 x0 h23 yd1 ffa fs9 fc3 sc0 ls0">!</div></div><div class="c x0 y0 w1 h0"><div class="t m7 x2c h23 y122 ffa fs9 fc3 sc0 ls0 ws11">( ,<span class="blank _2e"> </span>)</div></div><div class="c x3a y123 w10 h22"><div class="t m7 x0 h23 yd1 ffa fs9 fc3 sc0 ls0 ws12">(<span class="blank _2f"> </span>) !</div></div><div class="c x0 y0 w1 h0"><div class="t m7 x3b h25 y124 ffb fs9 fc3 sc0 ls0">n</div><div class="t m7 x3c h25 y125 ffb fs9 fc3 sc0 ls0 ws13">A n<span class="blank _11"> </span>m</div></div><div class="c x1c y123 w11 h22"><div class="t m7 x0 h25 yd1 ffb fs9 fc3 sc0 ls0 ws14">n m</div></div><div class="c x0 y0 w1 h0"><div class="t m7 x3d h26 y122 ffc fs9 fc3 sc0 ls7">=<span class="ls0 v2">−</span></div><div class="t m1 x3e h10 y126 ff8 fs3 fc3 sc0 ls0 ws0"> </div></div><div class="c x1 y127 w16 h2a"><div class="t m9 x0 h2b y128 ffa fsb fc3 sc0 ls0 ws22">8!<span class="blank _40"> </span>8!<span class="blank _1c"> </span>8 7<span class="blank _2e"> </span>6 5 4 3 2<span class="blank _3d"> </span>1</div></div><div class="c x0 y0 w1 h0"><div class="t m9 x47 h2b y89 ffa fsb fc3 sc0 ls0 ws23">(8<span class="blank _41"></span>, 5<span class="blank _0"></span>)<span class="blank _42"> </span><span class="ws24 v2">(8<span class="blank _2e"> </span>5) !<span class="blank _1c"> </span>3<span class="blank _0"></span>!<span class="blank _43"> </span>3<span class="blank _44"> </span>2<span class="blank _3d"> </span>1</span></div><div class="t m9 x47 h2b y129 ffa fsb fc3 sc0 ls0 ws22">(8<span class="blank _41"></span>,<span class="blank _f"> </span>5<span class="blank _0"></span>)<span class="blank _45"> </span>8 7<span class="blank _46"> </span>6 5 4<span class="blank _47"> </span>6720</div><div class="t m9 x44 h2c y12a ffb fsb fc3 sc0 ls0">A</div><div class="t m9 x44 h2c y129 ffb fsb fc3 sc0 ls0">A</div></div><div class="c x48 y12b w17 h2d"><div class="t m9 x0 h2e y12c ffc fsb fc3 sc0 ls0 ws25">×<span class="blank _3d"> </span>×<span class="blank _3d"> </span>× ×<span class="blank _48"> </span>× ×<span class="blank _44"> </span>×</div></div><div class="c x0 y0 w1 h0"><div class="t m9 x30 h2e y89 ffc fsb fc3 sc0 ls0 ws26">=<span class="blank _28"> </span>= =</div><div class="t m9 x1 h2e y12d ffc fsb fc3 sc0 ls0 ws27">−<span class="blank _49"> </span>× ×</div><div class="t m9 x30 h2e y129 ffc fsb fc3 sc0 ls0 ws25">=<span class="blank _48"> </span>×<span class="blank _44"> </span>×<span class="blank _3d"> </span>× ×<span class="blank _3b"> </span>=</div><div class="t m1 x49 h10 y12e ff8 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 xb hf y12f ff7 fs3 fc3 sc0 ls0 ws0">Resposta: C </div><div class="t m1 xb hf y130 ff7 fs3 fc3 sc0 ls0 ws0"> </div><div class="t m1 xb hf y131 ff7 fs3 fc7 sc0 ls0 ws0">1.4 <span class="blank _1"> </span>A<span class="blank _41"></span>rranjo com repe<span class="blank _1"> </span>tição </div><div class="t m1 xb h10 y132 ff8 fs3 fc3 sc0 ls0 ws0"> <span class="blank _7"> </span>Imagine <span class="blank _f"> </span>que <span class="blank _f"> </span>tem<span class="blank _1"> </span>os <span class="blank _f"> </span>à <span class="blank _f"> </span>disposição <span class="blank _f"> </span>as <span class="blank _f"> </span>le<span class="blank _1"> </span>tras <span class="blank _f"> </span>A, <span class="blank _f"> </span>B, <span class="blank _f"> </span>C <span class="blank _f"> </span>e <span class="blank _f"> </span>D. <span class="blank _f"> </span>Qu<span class="blank _1"> </span>eremos <span class="blank _f"> </span>utilizá-las </div><div class="t m1 xb h10 y133 ff8 fs3 fc3 sc0 ls0 ws0">para <span class="blank _9"> </span>form<span class="blank _1"> </span>ar <span class="blank _a"> </span>p<span class="blank _1"> </span>lacas <span class="blank _9"> </span>de <span class="blank _9"> </span>carros. <span class="blank _12"> </span>Assim, <span class="blank _9"> </span>precisamos <span class="blank _9"> </span>de <span class="blank _9"> </span>formar <span class="blank _12"> </span>grupos <span class="blank _9"> </span>de <span class="blank _9"> </span>3 <span class="blank _12"> </span>letras, </div><div class="t m1 xb h10 y134 ff8 fs3 fc3 sc0 ls0 ws0">sendo que essa<span class="blank _1"> </span>s letras podem se<span class="blank _1"> </span>r repetidas. Isto é, po<span class="blank _1"> </span>demos ter placas como:<span class="blank _1"> </span> AAA, </div><div class="t m1 xb h10 y135 ff8 fs3 fc3 sc0 ls0 ws0">AAB, ABA, BAA, ABC etc. </div></div><div class="t m0 x4 h5 y5 ff2 fs2 fc0 sc0 ls0 ws0">10323012795 - Rosamaria Domingues de Oliveira</div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div>
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