SOLUTION: 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 ?

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Question 548259: 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 ?
Answer by mathie123(224) About Me  (Show Source):
You can put this solution on YOUR website!
If there are AT LEAST three men on the committee, this means there could be 4 or 5 men. We will look at each case.
If there are 3 Men and 2 Women.
There are %287C3%29 ways to pick the 3 men (note it is a combination as order does not matter).
There are %286C2%29 ways to pick the 2 women (again, order doesn't matter)
These two things are done at the same time, so we can use the product rule.
%287C3%29%286C2%29

If there are 4 men and 1 woman
There are %287C4%29 ways to pick the 4 men (note it is a combination as order does not matter).
There are %286C1%29 ways to pick the 1 woman (again, order doesn't matter)
These two things are done at the same time, so we can use the product rule.
%287C4%29%286C1%29
If it is all men
There are %287C5%29 ways to pick the 5 men.


Now, we can add all these three options up and get our final answer. I will let you do this.
If you are unsure of answer please feel free to let me know:)