Problem Solving

BTGmoderatorLU wrote:Source: Economist GMAT

Private Benjamin is a member of a squad of 10 soldiers, which must volunteer 4 of its members for latrine duty. If the members of the latrine patrol are chosen randomly, what is the probability that Private Benjamin will be chosen for latrine duty?

A. 1/10
B. 1/5
C. 2/5
D. 3/5
E. 4/5

The OA is C

The number of ways 4 people can be chosen from 10 is 10C4 = 10! / [4!(10-4)!] = (10 x 9 x 8 x 7) / (4 x 3 x 2 x 1) = 10 x 3 x 7.

If Private Benjamin must be 1 of the 4 people chosen, then we have to choose 3 people from the remaining 9 people. The number of ways 3 people can be chosen from 9 is 9C3 = 9! / [3!(9-3)!] = (9 x 8 x 7) / (3 x 2 x 1) = 3 x 4 x 7.

Thus, the probability that Private Benjamin will be chosen for latrine duty is:

9C3 / 10C4 = (3 x 4 x 7) / (10 x 3 x 7) = 4/10 = 2/5

Answer: C