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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 -

    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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