Posted by **Dylan** on Tuesday, September 11, 2012 at 11:44pm.

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?

- Math -
**Steve**, Wednesday, September 12, 2012 at 11:25am
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

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