A committee of 5 people is to be chosen at random from 9 faculty members, with no repeats. Note that order does not matter.

a) How many possible committee memberships are there?

b) Assume that we have selected our 5 committee members. Now, we need to identify a chair and vice chair for the committee. How many possible chair and vice chair designations can be made from our 5 committee members. Note that the order of chair and vice-chair matters, and that they can't be the same person.

c) In total, how many possible committees, with chair and vice-chair designated, can we select from our original 9 faculty members?