Eight dice summing to twelve

Eight fair $6$ -sided dice are thrown. The probability that their faces sum to $12$ can be written as $\dfrac{x}{6^{8}}$ . Find $x$ .

Show hints (2)+

Let $d_i = 1 + e_i$ ; you need $\sum e_i = 4$ with $e_i\ge0$ (the cap $\le 5$ can't bind).
Stars and bars: $\binom{11}{7}=\binom{11}{4}=330$ .

Answer

Reveal answer →

330

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