Four dice summing to twenty

Four fair $6$ -sided dice are rolled. What is the probability their sum is exactly $20$ ?

Show hints (2)+

Reflect each die $x\mapsto 7-x$ : summing to $20$ has the same count as summing to $8$ .
Ways to sum to $8$ with four dice is $\binom{7}{3}=35$ (stars and bars); divide by $6^4$ .

Answer

Reveal answer →

0.027 (± 0.001)

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