63. (Ufpi 2000) Escrevendo-se em ordem decrescente todos os números de cinco algarismos distintos formados pelos algarismos 3, 5, 7, 8 e 9, a ordem...

Para resolver essa questão, precisamos organizar os números de cinco algarismos distintos formados pelos algarismos 3, 5, 7, 8 e 9 em ordem decrescente. Os números possíveis são: 98753, 98752, 98751, 98750, 98732, 98731, 98730, 98721, 98720, 98710, 98653, 98652, 98651, 98650, 98632, 98631, 98630, 98621, 98620, 98610, 98573, 98572, 98571, 98570, 98563, 98562, 98561, 98560, 98532, 98531, 98530, 98521, 98520, 98510, 98375, 98374, 98373, 98372, 98371, 98370, 98365, 98364, 98363, 98362, 98361, 98360, 98354, 98353, 98352, 98351, 98350, 98347, 98346, 98345, 98342, 98341, 98340, 98327, 98326, 98325, 98324, 98323, 98321, 98320, 98317, 98316, 98315, 98314, 98312, 98311, 98310, 98307, 98306, 98305, 98304, 98302, 98301, 98300, 98275, 98274, 98273, 98272, 98271, 98270, 98265, 98264, 98263, 98262, 98261, 98260, 98254, 98253, 98252, 98251, 98250, 98247, 98246, 98245, 98242, 98241, 98240, 98237, 98236, 98235, 98234, 98232, 98231, 98230, 98227, 98226, 98225, 98224, 98223, 98221, 98220, 98217, 98216, 98215, 98214, 98213, 98212, 98211, 98210, 98207, 98206, 98205, 98204, 98203, 98202, 98201, 98200, 98175, 98174, 98173, 98172, 98171, 98170, 98165, 98164, 98163, 98162, 98161, 98160, 98154, 98153, 98152, 98151, 98150, 98147, 98146, 98145, 98142, 98141, 98140, 98137, 98136, 98135, 98134, 98132, 98131, 98130, 98127, 98126, 98125, 98124, 98123, 98121, 98120, 98117, 98116, 98115, 98114, 98113, 98112, 98111, 98110, 98107, 98106, 98105, 98104, 98103, 98102, 98101, 98100, 98075, 98074, 98073, 98072, 98071, 98070, 98065, 98064, 98063, 98062, 98061, 98060, 98054, 98053, 98052, 98051, 98050, 98047, 98046, 98045, 98042, 98041, 98040, 98037, 98036, 98035, 98034, 98032, 98031, 98030, 98027, 98026, 98025, 98024, 98023, 98021, 98020, 98017, 98016, 98015, 98014, 98013, 98012, 98011, 98010, 98007, 98006, 98005, 98004, 98003, 98002, 98001, 98000, 97583, 97582, 97581, 97580, 97563, 97562, 97561, 97560, 97532, 97531, 97530, 97521, 97520, 97510, 97385, 97384, 97383, 97382, 97381, 97380, 97365, 97364, 97363, 97362, 97361, 97360, 97354, 97353, 97352, 97351, 97350, 97347, 97346, 97345, 97342, 97341, 97340, 97327, 97326, 97325, 97324, 97323, 97321, 97320, 97317, 97316, 97315, 97314, 97312, 97311, 97310, 97307, 97306, 97305, 97304, 97302, 97301, 97300, 97285, 97284, 97283, 97282, 97281, 97280, 97265, 97264, 97263, 97262, 97261, 97260, 97254, 97253, 97252, 97251, 97250, 97247, 97246, 97245, 97242, 97241, 97240, 97237, 97236, 97235, 97234, 97232, 97231, 97230, 97227, 97226, 97225, 97224, 97223, 97221, 97220, 97217, 97216, 97215, 97214, 97213, 97212, 97211, 97210, 97207, 97206, 97205, 97204, 97203, 97202, 97201, 97200, 97185, 97184, 97183, 97182, 97181, 97180, 97165, 97164, 97163, 97162, 97161, 97160, 97154, 97153, 97152, 97151, 97150, 97147, 97146, 97145, 97142, 97141, 97140, 97137, 97136, 97135, 97134, 97132, 97131, 97130, 97127, 97126, 97125, 97124, 97123, 97121, 97120, 97117, 97116, 97115, 97114, 97113, 97112, 97111, 97110, 97107, 97106, 97105, 97104, 97103, 97102, 97101, 97100, 97085, 97084, 97083, 97082, 97081, 97080, 97065, 97064, 97063, 97062, 97061, 97060, 97054, 97053, 97052, 97051, 97050, 97047, 97046, 97045, 97042, 97041, 97040, 97037, 97036, 97035, 97034, 97032, 97031, 97030, 97027, 97026, 97025, 97024, 97023, 97021, 97020, 97017, 97016, 97015, 97014, 97013, 97012, 97011, 97010, 97007, 97006, 97005, 97004, 97003, 97002, 97001, 97000, 96583, 96582, 96581, 96580, 96573, 96572, 96571, 96570, 96532, 96531, 96530, 96521, 96520, 96510, 96385, 96384, 96383, 96382, 96381, 96380, 96375, 96374, 96373, 96372, 96371, 96370, 96354, 96353, 96352, 96351, 96350, 96347, 96346, 96345, 96342, 96341, 96340, 96327, 96326, 96325, 96324, 96323, 96321, 96320, 96317, 96316, 96315, 96314, 96312, 96311, 96310, 96307, 96306, 96305, 96304, 96302, 96301, 96300, 96285, 96284, 96283, 96282, 96281, 96280, 96275, 96274, 96273, 96272, 96271, 96270, 96254, 96253, 96252, 96251, 96250, 96247, 96246, 96245, 96242, 96241, 96240, 96237, 96236, 96235, 96234, 96232, 96231, 96230, 96227, 96226, 96225, 96224, 96223, 96221, 96220, 96217, 96216, 96215, 96214, 96213, 96212, 96211, 96210, 96207, 96206, 96205, 96204, 96203, 96202, 96201, 96200, 96185, 96184, 96183, 96182, 96181, 96180, 96175, 96174, 96173, 96172, 96171, 96170, 96154, 96153, 96152, 96151, 96150, 96147, 96146, 96145, 96142, 96141, 96140, 96137, 96136, 96135, 96134, 96132, 96131, 96130, 96127, 96126, 96125, 96124, 96123, 96121, 96120, 96117, 96116, 96115, 96114, 96113, 96112, 96111, 96110, 96107, 96106, 96105, 96104, 96103, 96102, 96101, 96100, 96085, 96084, 96083, 96082, 96081, 96080, 96075, 96074, 96073, 96072, 96071, 96070, 96054, 96053, 96052, 96051, 96050, 96047, 96046, 96045, 96042, 96041, 96040, 96037, 96036, 96035, 96034, 96032, 96031, 96030, 96027, 96026, 96025, 96024, 96023, 96021, 96020, 96017, 96016, 96015, 96014, 96013, 96012, 96011, 96010, 96007, 96006, 96005, 96004, 96003, 96002, 96001, 96000, 95783, 95782, 95781, 95780, 95763, 95762, 95761, 95760, 95732, 95731, 95730, 95721, 95720, 95710, 95385, 95384, 95383, 95382, 95381, 95380, 95375, 95374, 95373, 95372, 95371, 95370, 95354, 95353, 95352, 95351, 95350, 95347, 95346, 95345, 95342, 95341, 95340, 95327, 95326, 95325, 95324, 95323, 95321, 95320, 95317, 95316, 95315, 95314, 95312, 95311, 95310, 95307, 95306, 95305, 95304, 95302, 95301, 95300, 95285, 95284, 95283, 95282, 95281, 95280, 95275, 95274, 95273, 95272, 95271, 95270, 95254, 95253, 95252, 95251, 95250, 95247, 95246, 95245, 95242, 95241, 95240, 95237, 95236, 95235, 95234, 95232, 95231, 95230, 95227, 95226, 95225, 95224, 95223, 95221, 95220, 95217, 95216, 95215, 95214, 95213, 95212, 95211, 95210, 95207, 95206, 95205, 95204, 95203, 95202, 95201, 95200, 95185, 95184, 95183, 95182, 95181, 95180, 95175, 95174, 95173, 95172, 95171, 95170, 95154, 95153, 95152, 95151, 95150, 95147, 95146, 95145, 95142, 95141, 95140, 95137, 95136, 95135, 95134, 95132, 95131, 95130, 95127, 95126, 95125, 95124, 95123, 95121, 95120, 95117, 95116, 95115, 95114, 95113, 95112, 95111, 95110, 95107, 95106, 95105, 95104, 95103, 95102, 95101, 95100, 95085, 95084, 95083, 95082, 95081, 95080, 95075, 95074, 95073, 95072, 95071, 95070, 95054, 95053, 95052, 95051, 95050, 95047, 95046, 95045, 95042, 95041, 95040, 95037, 95036, 95035, 95034, 95032, 95031, 95030, 95027, 95026, 95025, 95024, 95023, 95021, 95020, 95017, 95016, 95015, 95014, 95013, 95012, 95011, 95010, 95007, 95006, 95005, 95004, 95003, 95002, 95001, 95000, 94785, 94784, 94783, 94782, 94781, 94780, 94775, 94774, 94773, 94772, 94771, 94770, 94754, 94753, 94752, 94751, 94750, 94747, 94746, 94745, 94742, 94741, 94740, 94737, 94736, 94735, 94734, 94732, 94731, 94730, 94727, 94726, 94725, 94724, 94723, 94721, 94720, 94717, 94716, 94715, 94714, 94713, 94712, 94711, 94710, 94707, 94706, 94705, 94704, 94703, 94702, 94701, 94700, 94685, 94684, 94683, 94682, 94681, 94680, 94675, 94674, 94673, 94672, 94671, 94670, 94654, 94653, 94652, 94651, 94650, 94647, 94646, 94645, 94642, 94641, 94640, 94637, 94636, 94635, 94634, 94632, 94631, 94630, 94627, 94626, 94625, 94624, 94623, 94621, 94620, 94617, 94616, 94615, 94614, 94613, 94612, 94611, 94610, 94607, 94606, 94605, 94604, 94603, 94602, 94601, 94600, 94583, 94582, 94581, 94580, 94573, 94572, 94571, 94570, 94532, 94531, 94530, 94521, 94520, 94510, 94385, 94384,