Question

n!
Use:
n 'k k!(n-k)!
to solve the combination.
After a band parent meeting, each of
the ten members shook hands with
each other once. How many
handshakes were there in all?
Hint: Remember that one handshake involves
two people.
[?] handshakes

Answer 1

The question is asking how many combinations of two people can be made from a group of ten people.

Using the formula C(10,2) = 10!/(2! x (10 - 2)! = 10!/(2! x 8!) = 45 handshakes.

A simple way to prove this is each person shakes the hand of 9 other people
10 x 9 = 90 but this counts every handshake from the view of both people involved.
The actual number of handshakes is therefore 90 / 2 = 45