Top three dice summing to eighteen

Five fair $6$ -sided dice are rolled. What is the probability that the sum of the largest three values equals $18$ ?

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Three dice sum to $18$ only if all three are $6$ - so you need $\ge 3$ sixes among the five.
Binomial tail: $\sum_{k=3}^5\binom5k(1/6)^k(5/6)^{5-k}=276/7776$ .

Answer

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0.0355 (± 0.001)

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