Since there's four times three, I guess you could say possible handshakes. And what I'd like you to do is think a little bit about whether this is right, whether there would actually be 12 handshakes. Well, you might have thought about it, and you might say, well, you know, this four times three, this would count, this is actually counting the permutations. This is counting how many ways can you permute four people into two buckets, the two buckets of handshakers, where you care about which bucket they are in, whether they're handshaker number one or handshaker number two. This would count, this would count A being the number one handshaker and B being the number two handshaker as being different than B being the number one handshaker and A being the number two handshaker. But we don't want both of these things to occur. 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.