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

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

Given 7 women and 6 men:

For a WWWMM committee, there are 7 possibilities for the first woman, 6 for the second and 5 for the third, making 7*6*5 = 210 possible combinations. Similarly, there are 6*5 = 30 possible combinations for the men, giving an overall 210*30 = 6300 possible combinations of 3 women and 2 men.

The possible combinations for the other two committee makeups can be figured similarly and then add all 3 together for the total.