1. The problem statement, all variables and given/known data Since no one wants to answer my heat conductor problem (*hint hint*), here's a more interesting one. If it is assumed that all (52 choose 5) poker hands are equally likely, what is the probability of being deal one pair? (This occurs when the cards have denominations a, a, b, c, d, where a, b, c, and d are all distinct.) 2. Relevant equations Basic rules of probability 3. The attempt at a solution First, let me harken back to an example in the book and then employ the same reasoning. The book then goes on to say that we can think of this as a This gives the result (10 choose 5)*25 / (20 choose 5). Now, it seems like I can use an analogous 5-stage experiment. Stage 1: We'll have 4 different denominations represented. The number of ways to choose these is (13 choose 4). Stage 2: Then, from 1 of the chosen denominations, we'll have (4 choose 2) different suits to complete our pair. Stages 3-5: Then we'll choose 4 different suits from each of the remaining 3 denominations, which allows for 43 possibilities. Since the total number of ways to be dealt 5 cards from a deck of 52 is (52 choose 5), the probability of getting a single pair is therefore (13 choose 4) * (4 choose 2) * 43 / (52 choose 5). However, this isn't the answer in the back of the book. Explain my fallacious reasoning.