In how many ways can a committee of three men and four women be formed from a group of 9 men and 9women?
A) 10584
B) 1,524,096
C) 5040
D) 42

Question

Quizplus · Accepted Answer

The number of ways to choose 3 men out of 9 is $C(9,3) = \frac{9!}{3!(9-3)!} = 84$, and the number of ways to choose 4 women out of 9 is $C(9,4) = \frac{9!}{4!(9-4)!} = 126$. The total number of ways to form the committee is the product of these two, which is $84 \times 126 = 10584$.

In How Many Ways Can a Committee of Three Men