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Calculate the probability for 2 different digits in 4 cells.

  1. Jun 12, 2007 #1
    The set S={1,2,3,4}, there are 4 cells.
    What is the probability for 2 different digits (from S) to appear in 4 cells?
    Example:

    1,1,1,2 =>good
    3,4,4,3 =>good
    2,4,2,2 =>good

    1,2,3,4 =>not good
    1,2,3,3 =>not good
    1,1,1,1=>not good
     
  2. jcsd
  3. Jun 12, 2007 #2

    matt grime

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    Count those where you have 1 of one element 3 of another, and then 2 each of two elements.
     
  4. Jun 12, 2007 #3
    Well, the 3 elements:

    (4*3*2*3)/4^4

    4 possibilities to choose first number, 3 possibilities to choose second number,
    2 possibilities to choose third number and 3 possibilities to choose last number that has to be one of previous 3.

    Is it right ?
     
  5. Jun 12, 2007 #4

    matt grime

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    Doesn't seem at all right to me.
     
  6. Jun 25, 2007 #5

    ssd

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    This appears to be a home task. Since you have not informed that you got the solution, I am giving a broader hint.
    1st select the two to appear in the cells--- in 4C2 ways.
    For each of such choice find the no. of possible arrangements for the following cases.
    1/ both of them is arising twice
    2/ A specific no. of them arising thrice and the other once (and multiply this by 2,why?)
     
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