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What is the difference between the number of three-member committees that can be formed from a group of nine members and

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by Gmat_mission » Sun Jun 14, 2020 2:22 pm
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What is the difference between the number of three-member committees that can be formed from a group of nine members and the total number of ways there are to arrange the members of such a committee?

A. 0
B. 84
C. 252
D. 420
E. 504

[spoiler]OA=D[/spoiler]

Source: Princeton Review
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Re: What is the difference between the number of three-member committees that can be formed from a group of nine members

by Scott@TargetTestPrep » Sat Jun 20, 2020 2:40 pm
Gmat_mission wrote: ↑
Sun Jun 14, 2020 2:22 pm
 What is the difference between the number of three-member committees that can be formed from a group of nine members and the total number of ways there are to arrange the members of such a committee?

A. 0
B. 84
C. 252
D. 420
E. 504

[spoiler]OA=D[/spoiler]

Solution:

The number of 3-member committees that can be formed from 9 people (i.e., order doesn’t matter) is 9C3 = 9!/(3! x 6!) = (9 x 8 x 7)/3! = (9 x 8 x 7)/(3 x 2) = 3 x 4 x 7 = 84.

The number of ways to form the committees and arrange the members (i.e., order matters) is 9P3 = 9!/6! = 9 x 8 x 7 = 504.

Thus, the difference is 504 - 84 = 420.

Answer: D

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