Question

Twelve grad students have applied for three available teaching assistantships. In how many ways can the assistantships be awarded among these applicants if the group of applicants includes seven men and five women and it is stipulated that at least one woman must be awarded a scholarship?

Answer 1

Find this using the complement rule. So find the total number of ways the assistantships can be handed out and subtract the number of ways no woman is awarded the assistantship. This is the same as:

C(12,3)-C(7,4)