Solve the problem.
-A committee is to be formed consisting of 5 men and 3 women. If the committee members are to be chosen from 13 men and 14 women, how many different committees are possible?
A)2,220,075
B)1651
C)468,468
D)337,296,960

Question

Quizplus · Accepted Answer

The number of ways to choose 5 men out of 13 is $C(13,5)$ and the number of ways to choose 3 women out of 14 is $C(14,3)$. The total number of different committees is the product of these two, which is $C(13,5) \times C(14,3) = \frac{13!}{5!8!} \times \frac{14!}{3!11!} = 1287 \times 364 = 468,468$.

Solve the Problem. -A Committee Is to Be Formed Consisting of 5 Men