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Mon 12 Dec, 2011 01:19 pm
1. The ski club at Tula Tech has 35 members (15 females and 20 males). A committee of 3 members – a President, a Vice President, and a Treasurer – must be chosen.
a) How many different three-member committees can be chosen?
b) How many different three-member committees can be chosen if the president must be female?
c) How many different three-member committees can be chosen if the committee cannot have all females or all males?
@jon12,
a) 35! / 32! / 3!
b) 15 * 34! / 32! / 2!
c) (35! / 32! / 3!) - (15! / 12! / 3!) - (20! / 17! / 3!)
@engineer,
Since the committee members have distinct titles, I'd use permutations instead of combinations.
Part (b) kind of hints at that.
@markr,
I think you're right on that one. To the OP remove all the 3! and 2! values.
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