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Math Help - need prob. help fast

  1. #1
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    need prob. help fast

    Find the probability of rolling a total of 8 using 3 die.

    I want to do this without having to write down every option individually.

    Thanks for the help.
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  2. #2
    Eater of Worlds
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    The total number of combos is 6^{3}=216

    \left(\sum_{k=1}^{6}x^{k}\right)^{3}=(x+x^{2}+x^{3  }+x^{4}+x^{5}+x^{6})^{3}

    Can you expand this?. Look at the coefficient of the x term whose exponent is 8. That's the number of ways it's possible to sum to 8 with 3 dice.

    The expansion will start with x^3 and the first coefficient is 3. So, we have x^{3}+3x^{4}, thus far.

    Now, to find the next coefficient, multiply the coefficient of the x^4 term by the exponent 4 and divide by one less than the preceding exponent. (3)(4)/2=6

    x^{3}+3x^{4}+6x^{5}

    (6)(5)/3=10:

    x^{3}+3x^{4}+6x^{5}+10x^{6}

    Proceed in that manner a few more times and we get 21x^{8}

    The probability of rolling a sum of 8 with 3 dice is \frac{21}{216}=\frac{7}{72}
    Last edited by galactus; July 13th 2007 at 06:27 PM.
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