EXAMPLE 1.5.17

There are nine people on the Board of Directors of the Gomermatic Investment Corporation (GIC). At the onset of their monthly board meeting, each person shakes hands with each of the other people. How many handshakes occur?

SOLUTION

To form a handshake we need to select two different people from the set of nine people and have them shake hands. The order in which the two people are selected or listed is not important, since, for instance, if Homer shakes hands with Gomer itÕs the same as if Gomer shakes hands with Homer. Thus the number of handshakes is the number of ways to choose two people from a set of nine people if the order in which they are selected is not important:

C(9,2) = 36