We don't want A to shake B's hand where A is facing north and B is facing south, and then another time, they need to shake hands again where now B is facing north and A is facing south. We only have to do it once. These are actually the same thing, so no reason for both of these to occur. So we are going to be double counting. So what we really want to do is think about combinations. One way to think about it is you have four people. In a world of four people or a pool of four people, how many ways can you choose two?