A committee of 4 men and 3 women is to be chosen from a group of 11 men and 5 women. Determine the number of different ways of selecting the committee.
A)4
B)330
C)3,300
D)79,200

Question

Quizplus · Accepted Answer

The number of ways to choose 4 men out of 11 is $C(11,4) = \frac{11!}{4!(11-4)!}$, and the number of ways to choose 3 women out of 5 is $C(5,3) = \frac{5!}{3!(5-3)!}$. The total number of ways to form the committee is the product of these two, which is $C(11,4) \times C(5,3) = 330 \times 10 = 3,300$.

A Committee of 4 Men and 3 Women Is to Be