I solved a problem, by two different, and (apparently) viable solutions. But, each solution led me to a different answer: The question asks me to find out the number of possible ways in which I can choose 5 cards from a standard pack of 52 cards, so that I choose at least a single card from each suite. FIRST METHOD: One card from each suite of 13 means a total of [13C1 * 13C1 * 13C1 * 13C1]. After that, I'll have 52-4=48 cards left from which I need to choose only one. That means 48C1. The final result: 13C1 * 13C1 * 13C1 * 13C1 * 48 SECOND METHOD: I'll be choosing one card from three suites, but exactly two cards from the fourth suite. So that means: 13C1 * 13C1 * 13C1 * 13C2 = 13C1 * 13C1 * 13C1 * 13C2 * (12/2) And since I do this with each of the four suites (choose two from it only, while taking one from each of the others), I shall multiply this by 4, giving me: 13C1 * 13C1 * 13C1 * 13C2 * 24 And this is half of the answer arrived at by the first method.... . . . . . . . what went wrong????