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Math Help - Combinations & Permutations Help

  1. #1
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    Combinations & Permutations Help

    Hi, I just can't seem to figure this question out so here it is, any help would be greatly appreciated.

    Using a standard deck of cards, how many bridge hands (13 cards) contain 5 spades, 2 hearts, 3 diamonds and 3 clubs?
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  2. #2
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    Hello, gordomac!

    Using a standard deck of cards, how many bridge hands (13 cards)
    contain 5 spades, 2 hearts, 3 diamonds and 3 clubs?

    {13\choose5}{13\choose2}{13\choose3}{13\choose3} \;=\;\frac{13!}{5!\,8!}\cdot\frac{13!}{2!\,11!}\cd  ot\frac{13}{3!\,10!}\cdot\frac{13!}{3!\,10!}


    . . = \;1287\cdot 78 \cdot 286 \cdot 286 \;=\;8,211,173,256

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