I stumbled upon the following problem:
Given 'n' dice with 'm' faces with values 1 to m and a number 'x' what is the probability that the sum of the numbers on the 'm' dice is greater than or equal to 'x'? That is $m \le x \le n.m$ find $P(sum \ge x)$
Now, this 'almost approximates' a normal distribution. I'm sure it won't be a straight triangle but would have some sort of 'bell'-ish shape. Now the point is, "how" can I compute this without necessarily enumerating everything? Is there a generating function like thing I can use. Probably a recursive definition? Not sure if that's the way to go but I'm just at my wit's end. I was thinking of visualizing this distribution but that would still require to know the individual probabilities $P(sum = 6),...,P(sum = m.n)$
I've mostly encountered problems with 2-3 dice and it is somewhat easy to do or compute the sums. But how can one generalize this like in this problem?