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Grouping 12 people

  1. Nov 17, 2007 #1
    The number of ways in which 12 people may be divided into 3 equal groups is_
    My ans is 12C4*8C4*4C4=34650.
    But my test book contains the answer 5775.
    So iam confused. Is my answer correct or am i missing something?
     
  2. jcsd
  3. Nov 17, 2007 #2

    uart

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    Science Advisor

    Just that you are counting all possible orderings of the groups. What I mean is that if you have one particular grouping say { {1 2 3 4} {5 6 7 8} {9 10 11 12} } you are counting that same thing six times over (assuming that the ordering of the groups doesn't matter).

    { {1 2 3 4} {5 6 7 8} {9 10 11 12} }
    { {1 2 3 4} {9 10 11 12} {5 6 7 8} }
    { {5 6 7 8} {1 2 3 4} {9 10 11 12} }
    { {5 6 7 8} {9 10 11 12} {1 2 3 4} }
    { {9 10 11 12} {1 2 3 4} {5 6 7 8} }
    { {9 10 11 12} {5 6 7 8} {1 2 3 4} }

    You just need to divide your answer by six (3!) to correct this.
     
    Last edited: Nov 17, 2007
  4. Nov 18, 2007 #3
    Thank you uart.
     
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