10 people meet and shake hands. The maximum number of handshakes possible if there is to be no “cycle” of handshakes is (A cycle of handshakes is a sequence of k people a1, a2, ……, ak (k > 2) such that the pairs {a1, a2}, {a2, a3}, ……, {ak-1, ak}, {ak, a1} shake hands).\nOptions:\n(A) 7\n(B) 6\n(C) 9\n(D) 8\n(E) 10 Stream of consciousness first, then make a decision:
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The question is not written in proper manner but we can work in 3 methods\n1) If these are random handshakes, then total methods = 10*9/2*1 = 45\n2) If these are cyclic handshakes, then total methods = 10\n3) If these persons are not cyclic but they are arranged in a straight bench, then number of methods = 9
Thus, the answer is (C).
Assistant