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## Main Question or Discussion Point

How does one calculate the probability of a sum of r in the dice rolls of n dice? Can a probability distribution be written for something like this, to calculate the probability of a sum greater than r, greater than or equal to r, equal to r, less than or equal to r, less than r, etc.?

I do not want to simply brainstorm solutions leading to a sum of r, unless it is easy to generalize from there to n dice (which, from my consideration of n=2 and n=3, doesn't seem like the case - I need a more general way of thinking about it).

I do not want to simply brainstorm solutions leading to a sum of r, unless it is easy to generalize from there to n dice (which, from my consideration of n=2 and n=3, doesn't seem like the case - I need a more general way of thinking about it).