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Math Help - multinomial distribution , interpretation

  1. #1
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    multinomial distribution , interpretation

    1 . If a fair die is to be tossed 12 times , the probability of getting 1,2,3,4,5
    and 6 points exactly twice each is

    (apologies cant find decent latex software)
    0.166 = fraction 1 in 6


    (12! / 2!2!2!2!2!2! ) (0.166*2 ) (0.166*2) (0.166*2) (0.166*2) (0.166*2) (0.166*2) = 0.00344


    question 1

    does the formula used account for any order of the 2 of each ,meaning
    there is no order
    3 3 , 4 4 , 6 6 , 5 5 ,1 1, 2 2 is the same as
    1 1, 2 2, 3 3, 4 4, 5 5 , 6 6 and so on , it accounts for all the possible combinations of the 2
    of each ?.........

    if so ...

    question 2
    what would be the formula for the exact order
    the first is 1 , second is 1 , the third is 2 , the fourth is 2 etc in perfect running order?

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  2. #2
    MHF Contributor matheagle's Avatar
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    take away the factorials....

    \left({1\over 6}\right)^{12} by independence.
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  3. #3
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    struggling to understand what you mean.
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  4. #4
    MHF Contributor matheagle's Avatar
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    P(first is 1)=1/6 times P(second is 1 )=1/6 times P(third is 2)=1/6 times...
    I'm using independence and looking at the 12 tosses without using any formulas.
    the 12 choose 2,2,2,2,2,2 gives you all the rearrangements, here you aren't aking for that.
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  5. #5
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    1 * 12 = 2176782336
    ---
    6

    so a 1 in 2176782336 chance
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