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Math Help - How many 5-card hands make full house

  1. #1
    Senior Member Twig's Avatar
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    How many 5-card hands make full house

    Hi

    I have the feeling I am wrong somewhere, I try to calculate the number of 5-card hands that make full house.

    13\cdot \binom{4}{3}\cdot 12 \cdot \binom{4}{2}

    thanks
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  2. #2
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    Hello, Twig!

    I try to calculate the number of 5-card hands that make Full House.

    . . 13\cdot \binom{4}{3}\cdot 12 \cdot \binom{4}{2}

    . . \begin{array}{cc}\text{Number of values for the Triple:} & 13 \\<br />
\text{Number of ways to get the Triple:} & {4\choose3} \\ <br />
\text{Number of values for the Pair:} & 12 \\<br />
\text{Number of ways to get the Pair:} & {4\choose2} \end{array}

    Absolutely correct!

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