The way you can show this is;
(people labeled 1-6)
6 + 5 | 5 + 4 | 4 + 3 | 3 + 2 | 2 + 1
6 + 4 | 5 + 3 | 4 + 2 | 3 + 1
6 + 3 | 5 + 2 | 4 + 1
6 + 2 | 5 + 1
6 + 1 |
There are 30 possible combinations, but if they shake hands with every other person, the number is halved.
[tex] \frac{30}{2} =15[/tex]
This means that there are 15 handshakes total.
