SOLUTION: In how many ways can 5 men and 7 women make up a special committee if 5 persons are selected and at least 3 committee members must be women?

There can be either exactly 3 women, exactly 4 women, 
or exactly 5 women.


A.  Number of ways he can have 3 women and 2 men:

Choose the 3 women 7C3 ways and the 2 men 5C2 ways.
That's (7C3)(5C2) = (35)(10) = 350 ways.

B.  Number of ways he can have 4 women and 1 man:

Choose the 4 women 7C4 ways and the 1 man 5C1 ways.
That's (7C4)(5C1) = (35)(5) = 175 ways.

C.  Number of ways he can have 5 women and 0 men:

Choose the 5 women 7C5 ways and the 0 men 5C0 ways.
That's (7C5)(5C0) = (21)(1) = 21 ways.

Total = 350+175+21 = 546 ways.

Edwin