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# Probability

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If three, standard, 6-faced dice are rolled, what is the probability that the sum of the face up integers is 17?

Jul 3, 2022

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There are $$6 \times 6 \times 6 = 216$$ possibilities.

The only way to get a sum of 17 is to have a 6, 6, and 5, which can be done in $$3! \div 2 = 3$$ ways (divide by 2 because there are 2 6's)

So, the probability is $${3 \over 216} = \color{brown}\boxed{{1 \over 72}}$$

Jul 3, 2022