# Probability that two out of five cards are seven?

You are dealt five cards from 52 card deck that is thoroughly shuffled. What is the probability that two out of five cards are seven?

Is it: $${4C2 . 12C3 . (4C1)^3} / 52C5$$

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## 1 Answer

Kindly consult the Wikipedia page on Hypergeometric distribution. The correct formula is $$\frac{\binom{4}{2}\binom{48}{3}}{\binom{52}{5}}.$$ So $\binom{12}{3} \binom{4}{1}^3$ is incorrect.

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