text: are you smart? when two 6 sided dice numbered 1-6 and a 4 sided die numbered 1-4 are tossed, what is the probability that the sum of the three dice is divisible by 6? the total number of possibilities is 6*6*4 = 144 because you have 6 choices for the first, 6 choices for the second, and 4 choices for the third. the greatest sum you could possibly have is 6+6+4 = 16. thus, the only numbers that are less than or equal to 16 and divisible by six are 6 and 12. find the number of ways to roll a sum of 6 1,1,4 1,2,3 1,3,2 1,4,1 2,1,3 2,2,2 2,3,1 3,1,2 3,2,1 4,1,1 these are the only possiblities for 6 (you should check to make sure i didn't miss any.) number of ways to roll a sum of 6 is 10. ways to roll 12: 2,6,4 3,5,4 3,6,3 4,4,4 4,5,3 4,6,2 5,3,4 5,4,3 5,5,2 5,6,1 6,2,4 6,3,3 6,4,2 6,5,1 number of ways to roll twelve is 14 number of ways to have a sum of 6 or twelve = 10+14 = 24 answer: 24/144 = 1/6