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 in the committee. in how many ways can it be done?

a. 702
b. 624
c. 756
d. 812

Answer 1

To form a committee with at least 3 men out of a group of 7 men and 6 women, there are 735 ways to do so.

Step-by-step explanation:

To form a committee with at least 3 men out of a group of 7 men and 6 women, we can consider two cases: 1) Selecting exactly 3 men and 2 women or 2) Selecting 4 men and 1 woman.

Case 1: Selecting exactly 3 men and 2 women

The number of ways to select 3 men out of 7 is C(7, 3) = 35.

The number of ways to select 2 women out of 6 is C(6, 2) = 15.

Therefore, the total number of ways to form the committee in this case is 35 * 15 = 525 ways.

Case 2: Selecting 4 men and 1 woman

The number of ways to select 4 men out of 7 is C(7, 4) = 35.

The number of ways to select 1 woman out of 6 is C(6, 1) = 6.

Therefore, the total number of ways to form the committee in this case is 35 * 6 = 210 ways.

Adding the number of ways from both cases, we get a total of 525 + 210 = 735 ways.

So, the correct option is a. 735.