Suppose that 10 dice are rolled. Each dice is a regular 6 sided die with numbers 1 through 6 labelled on the sides. How many different sums of all 10 numbers are possible?
We can get any number from 10 to 60.
To see how many are possible look at this webpage.
The them $\displaystyle 85228x^{20}$ tells us that there are 85228 ways to roll a sum of 20.