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3 cards are chosen at random from a standard 52-card deck. What is the probability that they can be arranged into a group of three consecutive cards, all of the same suit? For this problem, an Ace can either come before a 2 or after a King, but not both (so A23 and QKA both count, but KA2 doesn't).

 Jun 22, 2022
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There are four suits, 12 different possible consecutive triples, and 6 ways to order 3 things, so the probability is

4*12*6/C(52,3) = 228/52100 = 72/5525.

 Jun 22, 2022

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