Three fair dice are rolled, and all outcomes are equally likely. What is the probability that the sum of all the numbers on the dice is at most 6?

Answer 1

If you count the dice as unique,
there are 6^3 = 216 possible outcomes
There are 42 where the sum is at most 6.
p(sum <= 6) = 42/216 = 7/36

1 1 1
1 1 2
1 1 3
1 1 4 and permutations: 24

1 2 2
1 2 3 and permutations: 12

2 2 2 and permutations: 6

If the dice are indistinguishable, then
there are 56 outcomes
there are 6 where sum <= 6
p(sum <= 6) = 6/56 = 3/28