Solve the problem.
-A committee of 4 men and 3 women is to be made from a group of 12 men and 8 women. In how many ways can such a committee be formed?
A) 551
B) 3,991,680
C) 27,720
D) 12,216

Question

Quizplus · Accepted Answer

The number of ways to choose 4 men out of 12 is $C(12, 4) = \frac{12!}{4!(12-4)!} = 495$, and the number of ways to choose 3 women out of 8 is $C(8, 3) = \frac{8!}{3!(8-3)!} = 56$. The total number of ways to form the committee is the product of these two, which is $495 \times 56 = 27,720$.

Solve the Problem. -A Committee of 4 Men and 3 Women Is to Women