Q: 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).
Options:
(A) 7
(B) 6
(C) 9
(D) 8
(E) 10
A: (C)
Explain how we arrive at this answer:
Explanation: The question is not written in proper manner but we can work in 3 methods
1) If these are random handshakes, then total methods = 10*9/2*1 = 45
2) If these are cyclic handshakes, then total methods = 10
3) If these persons are not cyclic but they are arranged in a straight bench, then number of methods = 9