Question

Eleven graduate students have applied for three available teaching assistantships. In how many ways can these assistantships be awarded among the applicants if the group of applicants includes six men and five women and it is stipulated that at least one woman must be awarded an assistantship?

Answer 1

3men, 1 women. for the first 2. and 2 men, 1 women for the third

Answer 2

The number of combinations, regardless of gender, is 11C3.
The number of combinations of men only is 6C3.
Therefore the required number of combinations is given by:
11C3 - 6C3 = 145