sandy wrote:

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

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 x 8 x 7 = 504.

Thus, the difference is 504 - 84 = 420.

Answer: D

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Jeffery Miller

Head of GRE Instruction

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