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).	Choose one:
A) 7  B) 6  C) 9  D) 8  E) 10
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= 
<gadget id="calculator">10*9/2*1</gadget>
<output>45</output>
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   ANSWER:9
<result>C</result>
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).