Say you have two 6 sided dice numbered from 1 to 6. How would you calculate the probability of rolling 2, 3, 4, ..., 12?
My professor told me the generating function $(x+x^2+x^3+x^4+x^5+x^6)^2$ is incorrect for starting the problem because the dice are treated as distinct. That I should be looking for the answer using identical dice and "sum". How would this be solved?