Everyone gets one of each

HardProbability Combinatorics~8m

A $12$ -card deck consisting of $4$ Kings, $4$ Queens, and $4$ Jacks (all $12$ cards distinct) is dealt evenly to $4$ players, $3$ cards each. What is the probability that every player receives exactly one King, one Queen, and one Jack?

Show hints (2)+

Total deals: $12!/(3!)^4$ ways to split into $4$ labelled hands of $3$ .
Favorable: give each rank's $4$ distinct cards one-per-player - $(4!)^3$ .

Answer

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0.0374 (± 0.001)

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Asked at: Jane Street, Citadel

Everyone gets one of each

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