Compute Probabilities Involving Permutations and Combinations
-In how many ways can a committee of three men and four women be formed from a group of 11 men and 11 women
A) 54450
B) 7,840,800
C) 554400
D) 110

Question

Quizplus · Accepted Answer

The number of ways to select a committee of three men from 11 men is $C(11, 3) = \frac{11!}{3!(11-3)!}$, and the number of ways to select a committee of four women from 11 women is $C(11, 4) = \frac{11!}{4!(11-4)!}$. The total number of ways to form the committee is the product of these two, which is $C(11, 3) \times C(11, 4) = 165 \times 330 = 54450$.