Determining dice probabilities

I have only managed to figure out how to do this with two dice by creating a result matrix and using countif() to find occurrences of a a particular sum.

I'm trying to create a formula, or whatever solution works, to determine what the probability of getting a certain sum on dice is.

Example: you roll 3 six sided dice and want to know the distribution of results for possibilities 3 through 18.

Also what if I want to change my dice to four six sided dice, but only keeping the highest three results? My range stays 3 to 18 but the mean and deviation should be higher and lower respectively.

Any thoughts?