(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Number of rolls with m many n-sided dice

How many different rolls are there with m many n-sided dice,if order is not important?

If order was important, the answer would simply be n^m. But if order is not important?

If two 6-sided dice are rolled, there are C(6,2)+C(6,1) = 21 different rolls.

If three 6-sided dice are rolled, there are C(6,3)+C(6,1)C(5,1)+C(6,1) = 56 different rolls.

Is there a general method for rolling m many n-sided dice? Or do you have to continue adding up all the cases? Perhaps a general method involving a matrix with m indices (e.g. a tensor) and simply excluding all permutations of the indices?

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# Number of rolls with m many n-sided dice

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