Solve the problem.
-A committee is to be formed consisting of 2 men and 3 women. If the committee members are to be chosen from 13 men and 9 women, how many different committees are possible?
A) 6,552
B) 78,624
C) 26,334
D) 162

Question

Quizplus · Accepted Answer

The number of ways to choose 2 men out of 13 is $C(13, 2) = \frac{13!}{2!(13-2)!} = 78$. The number of ways to choose 3 women out of 9 is $C(9, 3) = \frac{9!}{3!(9-3)!} = 84$. The total number of different committees is the product of these two, which is $78 \times 84 = 6,552$.

Solve the Problem. -A Committee Is to Be Formed Consisting of 2 Men