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 itÍs 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