posted by Ken on .
Please help. Thank you
Fourteen people attend a meeting. If each person shook hands with every other person, how many handshakes were there altogether?
In combination notation, that would be
C(14,2) = 14!/(12!2!) or 91
Each of the 14 people can shake hands with 13 other people, that would be 14x13 = 182 handshakes.
But that would be all cases of A shaking with B and B shaking with A, that is, we care counting each handshake twice.
So divide the 182 by 2 to get 91