Eleven graduate students have applied for two available teaching assistantships. In how many ways can these assistantships be awarded among the applicants if

Question

(a) No preference is given to any one student?
(c) The group of applicants includes seven men and four women and it is stipulated that at least one woman must be awarded an assistantship?

Answer 1

(a) N = 11 choose 2 (=11C2)
(c) 11 choose 2 less 7 choose 2, i.e.
N minus number of ways of choosing two men.