Exactly one pair

From a shuffled 52-card deck you deal a 5-card hand. What is the probability of getting exactly one pair (one rank appearing twice, the other three cards of distinct different ranks)? (to 3 decimals)

Show hints (2)+
  1. Choose the paired rank, then its suits, then the three off-ranks.
  2. Divide by C(52,5).

Answer

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0.423 (± 0.01)

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