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
(c) a majority of women
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
