1. The problem statement, all variables and given/known data When drawing a poker hand (5 cards), what is the probability to get a single pair? 3. The attempt at a solution This is my (wrong) line of thought: The first draw can be any card, so you have 52 options. For each of these cards you have 3 options to get a pair, so 52*3 in total ways to draw a pair. Now, for each of these 52*3 ways to draw a pair, you got 48*47*46 ways to draw the remaining cards. This makes a total of 52*3*48*47*46 ways to draw, and thus the probability for a pair is P=(52*3*48*47*46)/(52*51*50*49*48)=1/17. 1/17 is obviously wrong, but why is my logic wrong? Does it have something to do with the order the cards are drawn in?