A committee of 4 people is chosen from 9 women and 9 men. How many different committees are possible that consist of 2 women and 2 men?

Question

A committee of 4 people is chosen from 9 women and 9 men. How many different committees are possible that consist of 2 women and 2 men?

Answer 1

The simplest way to look at this is to start with men and women separately.

The number of combinations of 2 out of a group of 9 is expressed as:

 

₉C₂ = 36    This is the same for each.

 

So for every one combination of women, there are 36 combinations of men

to choose from. The total then is:

 

36 * 36 = 1296