Understanding the Handshake Problem I need help with this problem. The problem goes like this: In some countries it is customary to shake hands with everybody in the meeting. If there are two people there is 1 handshake, if there are three people there are three handshakes and so on. I know that the formula is $ \dfrac{n(n-1)}{2} $ but how do I get to this solution using a thinking process, specifically how would you solve this? Thanks.

If there exists $n$ people, then each person can shake hands with $n-1$ others. Each handshake gets counted twice. So ....
