SOLUTION: There are 7 women and 5 men in a department. Four people are needed for a committee. a) In how many ways can a committee of 4 people be selected? b) In how many ways can this com

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Question 1150200: There are 7 women and 5 men in a department. Four people are needed for a committee.
a) In how many ways can a committee of 4 people be selected?
b) In how many ways can this committee be selected if there must be exactly 2 men and 2 women on the committee?
c) In how many ways can this committee be selected if there must be at least 2 women on the committee?
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
a) In how many ways can a committee of 4 people be selected?

12C4 = 12%21%2F%284%21%2A8%21%29 = 495

b) In how many ways can this committee be selected if there must be exactly 2 men and 2 women on the committee?

7C2 * 5C2 = %287%21%2F%282%21%2A5%21%29%29%2A%285%21%2F%282%21%2A3%21%29%29 = 210

c) In how many ways can this committee be selected if there must be at least 2 women on the committee?

Ways to choose 4 women and 0 men: 7C4 = %287%21%2F%284%21%2A3%21%29%29 = 35
Ways to choose 3 women and 1 man: 7C3 * 5C1 = %287%21%2F%283%21%2A4%21%29%29%2A%285%21%2F%281%21%2A4%21%29%29 = 175
Ways to choose 2 women and 2 men: 7C2 * 5C2 = %287%21%2F%282%21%2A5%21%29%29%2A%285%21%2F%282%21%2A3%21%29%29 = 210
35 + 175 + 210 = 420