Four dice adding up to twenty

Four fair six-sided dice are thrown together. Find the probability that their total is exactly $20$.

$35/1296$. Write each die as $7-y_i$; then the $y_i\in\{1,\dots,6\}$ sum to $8$. Positive solutions of $y_1+\dots+y_4=8$ number $\binom73=35$, and none exceed $6$, so the probability is $35/6^4$.