SOLUTION: Suppose that there are 7 women and 5 men in a department. a). How many ways a committee of 4 people can be selected if there must be 2 men and 2 women? b). How many

Question 1142801: Suppose that there are 7 women and 5 men in a department.
a). How many ways a committee of 4 people can be selected if there must be 2 men and 2 women?
b). How many ways a committee of 4 people be selected if there is no requirement for number in regards to gender?
c). How many ways can a committee of 4 people be selected if there must be at least 1 man?
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

(a) Need to choose 2 of the 7 women AND 2 of the 5 men: (7C2)*(5C2)

(b) Can choose any 4 of the 12 total: (12C4)

(c) Can choose any combination EXCEPT 4 women and 0 men: (12C4) - (7C4)*(4C0)

You need to know the "n choose r" concept if you are going to be working problems like this. If you aren't familiar with it, searching the internet for "n choose r" will find hundreds of places where you can find it explained.
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