I'm trying to figure out what the probability of two people in a room sharing a birthday is, if there are 19 people in the room. Originally i assumed that the chances of any pair of people sharing a birthday are 1/365. Since there are 19c2 pairs of people in the room in question, I thought the probability was 19c2/365. This is obviously wrong though, since if the number of pairs in the room was >365, this type of reasoning would yield probabilities greater than one. Can anyone point me towards the right answer?