My question is a bit simplified due to space constraints, but I'll expand.
Here is my problem: I'm trying to calculate the odds a specific combination of dice. If I roll a die 6 times, what odds of a specific set of rolls. That's an easy enough problem, but the complication is that the numbers I can get on each roll can vary.
For example:
On roll 1, I can get a 1 or a 2 On roll 2, I can get any number but 6 On roll 3, I can only get the number 1 On roll 4, I can get the numbers 1 - 3 Etc...
Now I've been doing this sort of manually. Multiplying the fractions together, to get the odds of it. But it seems like there should be a simpler way, and I just can't figure it out. I've got a bunch of combos to churn through, and will do it manually if I have to, but am trying to save some time!
Forgive my math ignorance, and thanks!
The probability of getting any individual result from a set ${d_1,..,d_n}$ of results from one dice|roll is: $$ \frac n6 $$
Hence the probability of getting any individual result from a set ${d_{1},..,d_{n_i}}$ for the dice|roll $i$ from 1 to N dices|rolls is: $$ \prod_{i=1}^N\frac {n_i}6 $$
For example, the probability of getting 1 from dice|roll 1 and 2,3,4 or 5 from dice|roll 2 is ${4 \over 36}$