We want to select a committee of five members from a group of seven women and six men. The order of selection is irrelevant.

Question

We want to select a committee of five members from a group of seven women and six men. The order of selection is irrelevant.

How many committees can we make with fewer men than women? Suggestion: There could be three women and two men, four women and one man, or five women.

 committees

Answer 1

Your committee will have 0 men, 1 man or 2 men

The number of ways to select those committees is:

₇C₅ + 6*₇C₄ + 15*₇C₃

This is the hypergeometric distribution and the terms with C are the binomial coefficients.