Probability of three of a kind

MediumProbability Combinatorics~5m

A $5$ -card hand is dealt from a standard $52$ -card deck. What is the probability of exactly three of a kind - three cards of one rank and two cards of two different other ranks (not a full house, not four of a kind)? Round to four decimal places.

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Pick the triple's rank and $3$ of its $4$ suits, then two distinct kicker ranks with a suit each.
Favorable $= 13\cdot\binom{4}{3}\cdot\binom{12}{2}\cdot4^2$ ; divide by $\binom{52}{5}$ .

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0.0211 (± 0.0002)

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Probability of three of a kind

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