GingerAle
Oct 14, 2018

#2**0 **

**Max, your monographic summary analysis on binomial theory is amazing! **It’s one of the best I’ve read anywhere.

It’s wonderful you have returned! I hope you stay around for awhile.

*I will let you figure out the rest*.

I don’t know if the OP student will choose to figure out the rest, but I sure as hell will.

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You may find this formula interesting.

\(\sum \limits_{k=0}^{m}\binom{n}{k} (-1)^k \binom{p – s*k – 1}{p – s*k – n} \leftarrow \text {where p is the point (sum) target, n is the # of die, }\\ \hspace {47mm} \text{s is the number of sides, and } m=\lfloor \dfrac{p-n}{s}\rfloor \\\)

This formula is from J. V. Uspensky’s Introduction to Mathematical Probability (1937).

This calculates the number of combinations for any given sum of pips on (N) number of dice with (S) sides, where each die-side has a unique number of pips from 1 to (S)

I posted it as part of a rhetorical troll post here: https://web2.0calc.com/questions/counting-question#r17

GA

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GingerAleApr 10, 2024