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Counting Techniques Question: Drawing 5 specific cards out of a deck

  1. Mar 31, 2012 #1
    1. The problem statement, all variables and given/known data

    We draw 5 cards out of a normal deck of 52 cards. No replacements.
    How many combinations have exactly one Jack, one Queen, one King?

    2. Relevant equations



    3. The attempt at a solution

    The solution = 49,920

    My attempts:

    I keep getting 99,840.

    So 4C1 Jack, 4C1 Queen, 4C1 King, then for remaining two cards 40 possible, then 39 possible.

    I go 4C1 x 4C1 x 4C1 x 40 x 39 = 99,840

    Are there combinations that are repeated somewhere then? :S
     
  2. jcsd
  3. Mar 31, 2012 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    After choosing 1 Jack, 1 Queen and 1 King you need to choose two more cards from 40. The number of ways of doing that =?

    RGV
     
  4. Mar 31, 2012 #3
    oh! thanks Ray! Why doesn't it work going 40 x 39 instead of 40C2? Does 40 x 39 not work because that takes into account order as being relevant?
     
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