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Math Help - Card arrangement problem.

  1. #1
    Junior Member
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    Card arrangement problem.

    So the problem goes like this:

    How many ways can a hand of five cards consisting of four cards from one suit and one card from another suit be drawn from a standard deck of cards?

    So I was all like:

    nCr(4, 13) * nCr(1, 13) because you can choose 4 from one suit of cards (which is 13 cards in total) and then 1 from the other...

    I get 9295 but the book is like no: the answer is not 9295...

    It is instead 111,540... So I'm all like ok:

    Lets try nCr(4, 13) * nCr(1,39) basically saying it is every other suite (52-13), but that did not give the right answer.

    And now I'm all stuck on this problem. Can you help me? Thanks in advanced.
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  2. #2
    Super Member

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    Hello, thyrgle!

    How many ways can a hand of five cards be drawn from a standard deck
    consisting of four cards from one suit and one card from another suit?

    We want a foursome and a singleton.

    There are 4 choices for the suit of the foursome.
    . . And there are: . _{13}C_4 \:=\:\frac{13!}{4!\,9!} \:= 715 choices for the four cards.

    There are 3 choices for the suit of the singleton.
    . . And there are: . _{13}C_1 \:= 13 choices for the singleton.

    Therefore, there are: . 4\cdot715\cdot3\cdot13 \:=\:111,\!540 possible hands.

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