A committee of 3 men and 2 women is to be chosen from a group of 11 men and 9 women. Determine the number of different ways of selecting the committee.
A)5,940
B)3
C)35,640
D)165

Question

Quizplus · Accepted Answer

The number of ways to choose 3 men out of 11 is $C(11,3) = \frac{11!}{3!(11-3)!} = 165$, and the number of ways to choose 2 women out of 9 is $C(9,2) = \frac{9!}{2!(9-2)!} = 36$. The total number of ways to form the committee is the product of these two, which is $165 \times 36 = 5,940$.

A Committee of 3 Men and 2 Women Is to Be