Dice probabilities

[Allen]

(04-29-2024 04:55 PM)Thomas Klemm Wrote:  \(
\begin{align}
(x^2+x+1)^5 &= x^{10} + 5 x^9 + 15 x^8 + 30 x^7 + 45 x^6 + 51 x^5 + 45 x^4 + 30 x^3 + 15 x^2 + 5 x + 1 \\
\\
p &= \frac{1 + 5 + 15 + 30}{3^5} \\
&= \frac{51}{243} \\
&= \frac{17}{81} \\
&\approx 0.20988
\end{align}
\)

@dm If you like this kind of wizardy with counting, which Mr. Klemm and others here are simply world-class at doing on any platform, may I suggest A book called "Generatingfunctionology" by Wilf ( HTML page with terms)?

Related (unevaluated) Youtube lectures.