Question

From a group of 7 men and 6 women, five persons are to be selected from committees so that at least 3 men are there on the committee.In how many ways it can be done

Answer 1

Since at least 3 men must be chosen, we consider all committees which include 3, 4, and 5 men, with 2, 1, and 0 women, respectively. That is, we want to add the number of ways to:

a. Choose 3 from 7 men and 2 from 6 women = (7C3)*(6C2) = 35*15 = 525

b. Choose 4 from 7 men and 1 from 6 women = (7C4)*(6C1) = 35*6 = 210

c. Choose 5 from 7 men and 0 from 6 women = (7C5)*(6C0) = 21*1 = 21

a+b+c= 756.

Your ans. Is 756.

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