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Combinations of poker hands

  1. Mar 4, 2008 #1
    In a varient of Poker each player is dealt a hand of 6 cards from a standard pack How many hands are there of each of the following types?

    Three pairs: Two cards of the same value. another 2 of a differnt value, and a 3rd paid of a third value. i.e Q(clubs) Q(diamonds) 6(hearts) 6(diamonds) 4(spades) 4(hearts)


    For my attempt I started with 13C3 + 12C3 +11C3 ... + 3C3 = 1001 different hands

    But this hasn't accounted for the differnt variation of suits, threre are 6 possible pairs of suits, so i multiply 1001 by 6?

    thanks for any help!
  2. jcsd
  3. Mar 5, 2008 #2
    noone? :(
  4. Mar 5, 2008 #3


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    Homework Helper

    Hi Firepanda! :smile:

    erm … 13C3 is the number of ways of choosing 3 cards out of 13 … but what did you think was the reason for adding 12C3 etc?

    Be systematic. One step at a time.

    First step: there have to be three different numbers (eg 2 5 Q).

    Second step: for each number, there have to be 2 cards of that number.

    Try it that way! :smile:
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