Problem statement: Each card in a certain deck has three letters on it. The first letter is either A, B, or C. The second letter is either D, E, F, or G. The third letter is either H, I, J, K, or L. Every possible combination is represented exactly once in the deck. Ergo, there are 3x4x5=60 cards in the deck. How can I determine the probability that a hand of X cards, drawn randomly from the deck, will include at least one of each of the letters?
Problem source: http://ask.metafilter.com/251265/Probability-and-a-rather-unique-deck-of-cards