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(4) Eight members attend a committee meeting. The committee members shake the hands of some of the other members, not necessarily all, and possibly none. No pair of members shakes twice. (a) What is the maximum number of handshakes that can take place? (b) If exactly 20 handshakes have taken place, in how many ways can this have occurred? (5) Let n be an odd integer greater than 1. How much is the sum: 1 1 012 Prove your answer.

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