Dice probabilities

[Thomas Klemm]

\(
\begin{align}
(x^2+x+1)^5 &= x^{10} + 5 x^9 + 15 x^8 + 30 x^7 + 45 x^6 + 51 x^5 + 45 x^4 + 30 x^3 + 15 x^2 + 5 x + 1 \\
\\
p &= \frac{1 + 5 + 15 + 30}{3^5} \\
&= \frac{51}{243} \\
&= \frac{17}{81} \\
&\approx 0.20988
\end{align}
\)