1. The problem statement, all variables and given/known data Suppose 5 cards are dealt at random from a well shuffled, 52 card deck. The hand can be thought of as a random sample size 5 from 52, with no replacement. What is: (a) P (4 aces) (b) P (3 aces and 2 kings) (c) P (4 of a kind) 2. Relevant equations I know the formula for 'combinations' (number of equally likely unordered outcomes, no replacement) is number of equally likely unordered outcomes = n CHOOSE k, where n is the total sample size and k is the amount you're sampling/taking out. 3. The attempt at a solution I know all of the solutions, I got them from my teacher, I just can't understand them at all! These are the solutions: (a) P (4 aces) = (4 choose 4) x (48 choose 1) / (52 choose 5) (b) P (3 aces and 2 kings) = (4 choose 3) x (4 choose 2) / (52 choose 5) (c) P (4 of a kind) = (13 choose 1) x (4 choose 4) x (48 choose 1) / (52 choose 5) (a) I thought I understood this. I see why you'd put (52 choose 5) on the bottom, since that's what you're doing overall. And I thought it was (4 choose 4) because you have a total of 4 aces and you want all 4 of them, and I thought it was (48 choose 1) because you have 48 cards left to choose from, and you only need 1. Is this right? (b) Again, I kind of understand this, applying my previous logic. You have 4 aces and need 3, you have 4 kings and need 2, and that's your total hand dealt, so you don't need any more. (c) I have no idea where this comes from. Any help would be greatly appreciated!