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Math Help - 5-card hand probability

  1. #1
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    Jul 2011
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    5-card hand probability

    How many 5-card hands contain two of one rank and three of another rank? What is the probability of being dealt such a hand?

    I am not actually taking any classes that cover probability at the moment, so I don't have a lot of background knowledge for this one. I am, however, covering inclusion/exclusion at the moment so I gave it a shot.

    There are 13 ranks and I need to choose 2:

    {13\choose 2}

    Once this has been done, I need to choose 2 from one rank:

    {4\choose 2}

    and 3 from the other rank:

    {4\choose 3}

    So there are:

    {13\choose 2}\times {4\choose 2}\times {4\choose 3} possible hands?

    My answer is different from the one provided, I'm not sure why...

    How do I calculate the probability of being dealt such a hand once I know how many possibilities there are? Is it just \frac{possibilities}{52\times 51\times 50\times 49\times 48} ?
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  2. #2
    Junior Member
    Joined
    Sep 2011
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    Re: 5-card hand probability

    List of poker hands - Wikipedia, the free encyclopedia

    Your question is specifically about getting a Full House. You can follow this as long as you know n\choose {r} = C_n^r
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