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Math Help - Help with question on a deck of cards please

  1. #1
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    Help with question on a deck of cards please

    Ok, well the question in my book says that there are 52 cards in a deck of cards. How many possibilities are there if we are to take 6 cards randomly out of the deck if 2 of them have to be face cards (king, queen, jack).
    Can someone please explain to me how to do this with the answer so I can verify? thank you

    I thought something like 40!/4! but that seems totally wrong -.-
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  2. #2
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    Hello, roushrsh!

    There are 52 cards in a deck of cards.
    How many possibilities are there if we are to take 6 cards randomly out of the deck
    if two of them have to be face cards (King, Queen, or Jack)?

    There are: . \begin{Bmatrix}\text{12 Face cards} \\ \text{40 Others} \end{Bmatrix}


    We want two Face cards: . {12\choose2} ways.

    And we want four Others: . {40\choose4} ways.


    If the question means exactly two Face cards, the answer is:

    . . \frac{12\!}{2!\,10!}\cdot\frac{40!}{4!\,36!} \;=\;66 \times 91,\!390 \;=\;6,\!031,\!740 possibilities.

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  3. #3
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    thank you very much
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