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Thread: Dice Problems - Permutations and Combinations

  1. #1
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    Dice Problems - Permutations and Combinations

    1.How many possible sums can you roll if you have the choice to use at most 3 dice? You must use at least one die.

    2.If you were to roll 5 dice each 5 times, how many possible outcomes are there?
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  2. #2
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    Re: Dice Problems - Permutations and Combinations

    Quote Originally Posted by Unrated063 View Post
    2.If you were to roll 5 dice each 5 times, how many possible outcomes are there?
    I agree that #1 is trivial. But I am not sure that the first reply is correct about #2.
    To me it clear that five dice are rolled five times. The sums on each roll are summed to give a total.

    This is the expansion of the generating function.
    Look at the exponents in that expansion, they range from $25\text{ to }150$
    Next look at the coefficient of each term. One of the terms is $130616265x^{35}$.
    From which we now know that there are $130616265$ ways to get the sum $35$.

    The sum of all the coefficients gives the total possible outcomes.
    Attached Thumbnails Attached Thumbnails Dice Problems - Permutations and Combinations-expansion.gif  
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