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?
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