Question

A committee of 4 people is chosen from 8 women and 8 men. How many different committees are possible that consist of 2 women and 2 men?

Answer 1

784

Explanation:

There are the binomial coefficient "8 choose 2", i.e. `(8!)/(2!6!) = 28` ways to choose 2 people from a set of 8 people. So, there are 28 ways to choose 2 men and 28 ways to choose 2 women. This means that there is `28^2 = 784` ways to choose both 2 men and 2 women.