Problem:
A club with five men and six women wish to form a committee. The number of men must be between 1 and 3 (inclusive), and the number of women must be between 2 and 4 (inclusive). How many different committees can be formed?
1 man and 2 women 5 * 6C2
1 man and 3 women 5 * 6C3
1 man and 4 women 5 * 6C4
2 man and 2 women 5C2 * 6C2
2 man and 3 women 5C2 * 6C3
2 man and 4 women 5C2 * 6C4
3 man and 2 women 5C3 * 6C2
3 man and 3 women 5C3 * 6C3
3 man and 4 women 5C3 * 6C4
Work all those out and add them together.