So a couple days ago three people all showed up to work wearing the same shirt. At first I thought this was just like the birthday problem, the probability at least 2 people in a room have the same birthday, but when I think more about it I think it's different. In the birthday problem, everyone chooses a birthday from the same 365 days. They all have the same sample space. In this shirt problem, let A=all the shirts that exist, B=the shirts person 1 owns, and C=the shirts person 2 owns. B and C will be subsets of A, but they may or may not be disjoint from each other. So when person 1 and 2 get up in the morning, they are likely sampling from different sample spaces. Does what I say make sense? So how would you find the probability at least two people show up with the same shirt?