In how many ways can a committee of three men and four women be formed from a group of 12 men and 12women?
A) 108,900
B) 15,681,600
C) 6,652,800
D) 165

Question

Quizplus · Accepted Answer

The number of ways to select 3 men out of 12 is $C(12,3) = \frac{12!}{3!(12-3)!} = 220$, and the number of ways to select 4 women out of 12 is $C(12,4) = \frac{12!}{4!(12-4)!} = 495$. The total number of ways to form the committee is the product of these two, which is $220 \times 495 = 108,900$.

In How Many Ways Can a Committee of Three Men