Five fair six-sided dice are rolled. The probability that the sum of the numbers facing up is less than or equal to 21.
There is only one way of getting a total of 5 from 5 dice , or 1+1+1+1+1 =5. Then there 5 ways of getting a 6, or 2+1+1+1+1, 1+2+1+1+1, 1+1+2+1+1, 1+1+1+2+1, 1+1+1+1+2......and so on for every number from 5 up to 21.
Then you add them all up like this:
1+5+15+35+70+126+205+305+420+540+651+735+780+780+735+651+540 =6,594 / 6^5 =~84.8% probability.
