Philip P. answered 09/13/15
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It's a permutation because the order matters. Suppose you pick Bob, Fred,and Alice - that's Bob for captain, Fred for co-captain, and Alice for secretary. I could choose the same three people as Alice, Bob, and Fred; but now Alice would be captain, Bob co-captain, and Fred secretary - a different result for the same 3 people. So the order people are chosen matters.
Mark M.
09/13/15