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).

a)7 b) 6 c) 9 d) 8

• Please note the condition mentioned in question i.e. k>2,
  If these persons are not cyclic but they are arranged in a straight bench, then number of methods = 9
  and with the condition k>2, the number of methods = 8
  
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