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?Choices:- 756 752 754 758

We can solve this problem by considering the different possible scenarios for the composition of the committee:

1. Scenario 1: The committee consists of 3 men and 2 women. The number of ways to select 3 men from 7 is "7 choose 3", and the number of ways to select 2 women from 6 is "6 choose 2". So, the total number of ways for this scenario is (7 choose 3) * (6 choose 2).

2. Scenario 2: The committee consists of 4 men and 1 woman. The number of ways to select 4 men from 7 is "7 choose 4", and the number of ways to select 1 woman from 6 is "6 choose 1". So, the total number of ways for this scenario is (7 choose 4) * (6 choose 1).

3. Scenario 3: The committee consists of all 5 men. The number of ways to select 5 men from 7 is "7 choose 5". There are no women in this scenario, so we don't need to consider them. So, the total number of ways for this scenario is (7 choose 5).

Adding up the total number of ways for each scenario gives us the total number of ways to form the committee.

Let's calculate:

1. (7 choose 3) * (6 choose 2) = 35 * 15 = 525
2. (7 choose 4) * (6 choose 1) = 35 * 6 = 210
3. (7 choose 5) = 21

So, the total number of ways to form the committee is 525 + 210 + 21 = 756.

Therefore, the answer is 756.