SOLUTION: In how many ways can a committee of 5 people be formed from a group of 10 if certain 3 men insist on serving together or not at all?

Question 391827: In how many ways can a committee of 5 people be formed from a group of 10 if certain 3 men insist on serving together or not at all?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Do this case by case.

Case 1: The three men serve together.
Then, there are only two people left to choose out of a group of 7, so 7C2, or 21 ways to choose two more people given this case.

Case 2: The three men don't serve.
Then, we choose 5 people out of the remaining 7, so 7C5, also equal to 21 ways (since nCr = nC(n-r), which can easily be shown algebraically).

Therefore the total number of ways is 21+21, or 42.
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