1
vote
1answer
45 views

Finding the coefficient of a generating function

Given $f(x) = x^4\left(\frac{1-x^6}{1-x}\right)^4 = (x+x^2+x^3+x^4+x^5+x^6)^4$. This is the generating function $f(x)$ of $a_n$, which is the number of ways to get $n$ as the sum of the upper faces of ...
1
vote
2answers
78 views

DICE - Rolling at least *k* on *n* six-sided dice - with a twist!

I am putting together a table of dice probabilities for a project I am working on and have found myself intimidated by a little "special case" I'm trying to work with. For determining the probability ...
2
votes
0answers
139 views

probability of rolling at least $n$ on $k$ 6-sided dice

Is there a simple form for the probability of rolling at least $n$ on $k$ 6-sided dice? Of course you can do it by recursion (see here). But is there a way to do it with just a few binomial ...
4
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1answer
199 views

Probability of a certain dice roll sum disregarding lowest rolls

The number of ways to obtain a total of $p$ in $n$ rolls of $s$-sided dice is: $$c=\sum_{k=0}^{\lfloor(p-n)/s\rfloor}(-1)^k\binom{n}k\binom{p-sk-1}{n-1}\;.$$ What I'm interested in is making the $n$ ...