The head of a large company has 9 close friends. a) In how many ways can he invite six of them to dinner?
b) Repeat a) if two of his friends are divorced, hate each other, and cannot both be invited.
c) Repeat a) if the friends consist of three single people and three married couples and if a husband or wife is invited, the spouse must be invited, too.
Part a is relatively straight forward. It would simply be C(9,6) since the order in which he invites them does not matter.
Part b and c are a little more complicated and I'm not sure how to do them. Any help would be appreciated.