How Many Possible Committees Can Be Chosen from a Group of 8 Men and 9 Women?

[duki]

Homework Statement

A committee of seven is to be chosen from 8 men and 9 women.
a) how many possible committees are there?
b) how many committees contain at least 6 woment?
c) if bob and alice cannot be on the same committee because they cannot work together well, how many committees are possible?

Homework Equations

The Attempt at a Solution

Not sure where to start really... other than writing down every possible committee

 

[Elucidus]

Hints:

(a) This is a combination, (8+9) choose 7.

(b) (committee of 7 with 6 women) + (committee of 7 with 7 women)

(c) (all committees) - (those with both Bob and Alice).

--Elucidus