What is the probability that the sum of 10 fair dice is divisible by 6?

Suppose we roll 10 fair standard dice. What is the probability that their sum is divisible by 6, assuming that the rolls are independent.

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September 1st, 2009 at 5:57 pm

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Whatever the first 9 dice come up,

there is only one possibility for the 10th.

So the probability is 1/6.

(Last die must be 6 – (other 9 mod 6)).

This holds for any number of dice.

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