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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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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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