19.Three-Card Straight from 8 Decks
★★★classical probabilityCh. 1 — Classical Probability and Combinatorics444+ Problems in Probability
8 standard 52-card decks are combined together and shuffled well. Find the probability that 3 cards drawn uniformly at random from this deck form a three-card straight (three consecutive ranks, with Ace counting as low or high). Straight flushes do not count.
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There are 12 rank sequences (A-2-3 through Q-K-A). With 8 decks there are 32 cards of each rank — and remember to subtract the straight flushes.
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