An ace for everyone

A standard 5252-card deck is shuffled and dealt evenly to 44 players (1313 cards each). What is the probability that each player receives exactly one ace? Round to four decimal places.

Show hints (2)+
  1. Place the four aces one by one; each new ace must land with a player who has no ace yet.
  2. The fractions are 395126501349\tfrac{39}{51}\cdot\tfrac{26}{50}\cdot\tfrac{13}{49} (the first ace is free).

Answer

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0.1055 (± 0.0003)

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Asked at: Jane Street, SIG

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