We have fair "m" sided "n" dice.
What is the probability (or/and probability density function) for obtaining the sum of numbers on dice "S"
after rolling them (together) "N" times. I need probability dependence on "N". "m","n" and "S" are parameters.
We must assume that the sides are numbered .
If you expand the polynomial the term tells us if we toss n m-sided dice then there are ways to get the sum .
Look at this webpage.
You see that models tossing five nine sided dice. The term tells us that there are 330 ways that the sum of the five will equal 38.
So .
From there on it is a simple matter of using binomial distribution on N trials.
The PDF independent of number of trials will be
Dice - Wikipedia, the free encyclopedia last expression in the section of "Probability"
Is that right? Is there a closed form expression which will also include number of trials "N"?