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How many different 5 card poker hands would contain only cards of a single suit?

I know there are 2,598,960 different 5 card poker hands but I don’t know how many would only contain a single suit.

4 Responses to “How many different 5 card poker hands would contain only cards of a single suit?”

  1. a²+b²=c² says:
    June 8, 2010 at 6:21 am

    There are 4 suits, and for each suit, 13 cards. You’re choosing 5 of them, so 4(13C5) = 5148 hands.

    You can also solve this by looking up the frequency of the types of hands in poker. What you want is the number of flushes plus straight flushes plus royal flushes.

  2. kro says:
    June 8, 2010 at 7:06 am

    5,108 it’s called a flush.

    36 straight flush

    4 royal flush

  3. Bob K says:
    June 8, 2010 at 7:16 am

    First, you choose which suit you want to have 5 cards of, so that would be 4C1, next, there are 13 cards in a suit and you want to choose 5 of those, or 13C5. And then multiply the two choices as they are independent
    4C1*13C5
    4!/3!1! * 13!/5!8!
    4 * 1287
    5148

  4. icemetalpunk says:
    June 8, 2010 at 7:54 am

    Think of it this way: There are 13 cards of a single suit. So find the number of combinations of 13 cards, no repetition. Then realize there are 4 suits, so multiply that number by 4.

    The formula for combinations is n!/(r!(n-r)!) where n=number of possible cards (13) and r=number of chosen cards (5). Substituting gives us:

    13!/(5!(13-5)!) = 13!/(120*8!)

    If we work this out, we get 1287. Now we remember there are 4 suits, and multiply this by 4 to get:

    5148 combinations.

    -IMP ;) :)

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