SOLUTION: A committee of 5 people is going to be chosen from a group of 8 women and 10 men. How many different committees are possible if the committee must contain at least 1 woman and at

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Question 1182280: A committee of 5 people is going to be chosen from a group of 8 women and 10
men. How many different committees are possible if the committee must
contain at least 1 woman and at least 1 man?
How many committees are possible if the committee must have 3 women and 2 men?
How many committees are possible if the committee must have more women than men?
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
A committee of 5 people is going to be chosen from a group of 8 women and 10
men.
There are 18 people choose 5 committee members.  that's 18C5 = 8568 ways to
select a committee of 5 people.
How many different committees are possible if the committee must contain at
least 1 woman and at least 1 man?
From the 8568 ways to choose 5 people, we must eliminate and subtract those
which 

1. contain only women.  That's 8 women choose 5 or 8C5=56 
2. contain only men.  That's 10 men choose 5 or 10C5=252 

That's 56+252=308 that we must subtract from the 8568.

Answer = 8568-308 = 8260.

Edwin
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