Suppose that a department contains 10 men and 17 women. How many ways are there to form a committee with 6 members if it must have strictly more women than men?

Answer 1

To choose 5 women and 1 man, there are
(17,5)*(10,1) ways.
Figure out the number of ways to choose
6 women,
4 women and 2 men,
and add up the total number of ways.