Question

Assume there are 10 people in a room, including you. each person in the room must shake hands one time, and only one time, with all the other people in the room. how many handshakes will occur?

Answer 1

You calculate the number of ways that 2 people can be chosen from 10.
The formula:
n! / r! * (n-r)! =
10! / 2! * 8! =
10 * 9 * 8! / 2 * 8! =
10 * 9 / 2 =
45 handshakes

Source:
http://www.1728.org/combinat.htm