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Math Help - Probability -dealing with cards

  1. #1
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    Probability -dealing with cards

    This question is on a final exam study sheet. Here it is: What is the probability of getting a full house ( 3 of one number and 2 of another) from 5 cards dealt from a shuffled deck of 52 playing cards?

    Not sure quite how to attack this ... permutation? combination? etc
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  2. #2
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    Quote Originally Posted by RotundRaspberry View Post
    This question is on a final exam study sheet. Here it is: What is the probability of getting a full house ( 3 of one number and 2 of another) from 5 cards dealt from a shuffled deck of 52 playing cards?

    Not sure quite how to attack this ... permutation? combination? etc
    Read this: Poker probability - Wikipedia, the free encyclopedia
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  3. #3
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    Hello, RotundRaspberry!

    Card games are usually combinations
    . . since the order of the cards makes no difference.


    What is the probability of getting a Full House (3 of one number and 2 of another)
    from 5 cards dealt from a shuffled deck of 52 playing cards?

    There are 13 choices for the value of the Triple.
    There are: . _4C_3 \,=\,{\color{blue}4} ways to get the Triple.

    There are 12 choices for the value of the Pair.
    There are: . _4C_2 \,=\,{\color{blue}6} ways to get the Pair.

    Hence, there are: . 13\cdot 4\cdot12\cdot 6 \;=\;{\color{blue}3,\!744} possible Full Houses.


    There are: . _{52}C_5 \;=\,2,\!598,\!960 possible 5-card Poker hands.


    Therefore: . P(\text{Full House}) \;=\;\frac{3744}{2,\!598,\!960} \;=\;\frac{6}{4165}

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