Question

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

A) 564 B) 735 C) 756 D) 657

Answer 1

Step-by-step explanation:

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. Hence option C

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