McMaster University is about to have a reunion of all the previous graduating classes from the last five years. There are nineteen members of the current alumni association, with four administrative staff members. Eight of the current members are also recent graduates.

a) In how many ways can a subcommittee offour be selected if three administrative staff members cannot serve on the committee due to prior engagements?

b) In how many ways can a subcommittee offour be selected if Ms. Dot must be on the committee or Mr. Yako along with Mr. Wacko must serve when she is not a chosen member? [Note: all three are administrative staff members.]

c) In how many ways can a subcommittee ofsix members be formed ifmore than half of its members must berecent graduates?