SOLUTION: A group of nine women and six men must select a four-person committee. How many committees are possible if it must consist of the following? (a) two women and two men (b) a

Question 949131: A group of nine women and six men must select a four-person committee. How many committees are possible if it must consist of the following?
(a) two women and two men

(b) any mixture of men and women

(c) a majority of women
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!
A group of nine women and six men must select a four-person committee.
How many committees are possible if it must consist of the following?
(a) two women and two men

Choose the 2 women 9C2 = 36 ways.
Choose the 2 men 6C2 = 15 ways

Tats 36*15 = 540 ways.

(b) any mixture of men and women

Since it must be a mixture, it can't be all men or all women.

We do this indirectly, but counting all possible four-person
commmittes, then counting the unacceptable ones, and subtracting.

There are 9+6=15 people.

So altogether there are 15C4 possible committees with 
no restrictions.

There are 9C4 unacceptable committes thatr consist of all women.
There are 6C4 unacceptable committes thatr consist of all men.

Answer 15C4 - 9C4 - 6C4 = 1365 - 126 - 15 = 1224

Case 1:  3 women and 1 man
Choose the 3 women 9C3
Choose the 1 man 6C1
That's 9C3*6C1 = 84*6 = 504

Case 2: All four are women
That's 9C4 = 126

Total:  504+126 = 630

Edwin

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