I previously posted a question, but unintentionally omitted some crucial details I only realized after it had already been answered.
As such, my question is this:
How do you calculate the probability of rolling $x$ or more with $k$ out of $m$ dice with $n$ sides?
- Example 1: Rolling one or more $6$s with three 6-sided dice.
- Example 2: Rolling two or more $6$s, $7$s or $8$s with six 8-sided dice.
- Example 3: Rolling three or more $7$s, $8$s, $9$s or $10$s with nine 10-sided dice.
I'm looking for a general function, but thus far have only been able to figure out $f(x)\to1-(\frac56)^x$ for Example 1.
While the answers of my previous question helped a great deal, any additional help would be appreciated.