I want to find the probability that a 5-card poker hand contains exactly four kinds. I don't understand the difference between the following answers, yet only the first one is right. Why is the second one wrong?
For me, it equates to: choose your 4 ranks from 13 cards. For every chosen kind, choose between the 4 suits (13 C 4 * 4^4). Then, choose one of the 4 previously chosen ranks (4 choices) and for that rank, choose one of the 3 remaining suits (* 3). Where do I count duplicates?