A committee of 4 men and 1 woman is to be chosen from a group of 11 men and 9 women. Determine the number of different ways of selecting the committee.
A)330
B)71,280
C)24
D)2,970

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 1 woman out of 9 is $C(9,1) = \frac{9!}{1!(9-1)!}$. The total number of ways to form the committee is the product of these two, which is $C(11,4) \times C(9,1) = 330 \times 9 = 2,970$.

A Committee of 4 Men and 1 Woman Is to Be