I have posted a similar problem not long ago.This time, I am trying to find a connection between 3 concepts that would possibly lead to the answer to the problem. I have heard that there is a way to find the probability of getting a particular sum by rolling multiple six-sided dice at the same time without listing ALL the outcomes which is really horrifying. Someone told me that there is a connection among polynomials, Pascal's triangle, combinations and dice. For example, say you roll 5 six-sided fair dice and want to find the probability of getting a sum of 17. In this case, there are 780 combinations of such a sum and 6^5 different sums. So, the probability of the sum of 17 is 0.100308641975309. That person said that you consider the polynomial expansion of (1+x+x^2+x^3+x^4+x^5)^5 . Each term is raised to ascending powers. The 6 terms in there represent the 6 sides of each die and the 5th power represents the 5 dice. If you can connect it to Pascal's triangle and combinations, you will get the correct answer as stated above. I am not sure if I wrote down the polynomial correctly. I lost contact with that person. Can someone tell me how it is possible to solve the 5 six-sided dice problem with those concepts? Thanks.