GRE-Math-Questions-to-Know-by-Test-Day-2nd-Edition_pag206

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 The order in which committee members are selected is immaterial. Therefore, the num-
ber of distinct committees is:
 C20 3 = 
−
20!
(20 3)!3!
 = 
20!
(17)!3!
 = 20 19 18
3 2 1
1,140
⋅ ⋅
⋅ ⋅
= 
227. 2,700 Applying the fundamental counting principle to four tasks (refer to 
Answer 96) yields 30 6 3 5 2,700⋅ ⋅ ⋅ = different shoes in stock.
228. 24,360 There are 30 ways to fill the first position. After that position is filled, there 
are 29 ways to fill the second position. After the first and second positions are filled, there 
are 28 ways to fill the third position. Thus, there are ⋅ ⋅ =30 29 28 24,360 different ways to 
fill the positions.
229. 64 Because repetitions are allowed, there are 4 ways to select the first digit, 4 ways 
to select the second digit, and 4 ways to select the third digit, yielding ⋅ ⋅ =4 4 4 64 possible 
three-digit codes.
230. 60 For a 3-digit number, you must fill the hundreds place, the tens place, and the 
ones place. To be greater than 700, the hundreds digit must be 7, 8, or 9. Thus, there are 
three choices for the hundreds digit. After the hundreds digit is selected, 5 digits are avail-
able for the tens place. After the tens place is selected, 4 digits are available for the ones 
place. Therefore, there are ⋅ ⋅ =3 5 4 60 such numbers.
231. 2 Let b = the number of boys in the family and g = +b 2 = the number of girls in the 
family. The total number of children is + + = +b b b( 2) 2 2. The probability, P, of randomly 
selecting a girl is:
 = = +
+
=P b
b
number of girls
number of children
2
2 2
2
3
 
 Solve for b.
 +
+
=b
b
2
2 2
2
3
 + = +b b3( 2) 2(2 2) 
 + = +b b3 6 4 4 
 b = 2
232. 0.32 There are two ways for Katniss to make exactly one of the next two foul shots. 
She can make the first foul shot, but miss the second foul shot, or she can miss the first foul 
shot, but make the second foul shot. The probability that Katniss will make the shot is 0.8 
and the probability that she will miss is 0.2. The outcomes of the foul shots are independent, 
so the probability that Katniss will make exactly one of the next two foul-shot attempts is 
+(0.8)(0.2) (0.2)(0.8) = 0.32.
06_McCune_Answer.indd 197 2/21/22 4:48 PM