I'm trying to work on a project in code that asks this question. I'm currently able to get the right answer by breaking it up, but I'm wondering if there's a mathematical formula I can address this problem to as I'm actually facing computational resource limitations.
For example, the amount of combinations for 50 dice is 50^6, which is 15,625,000,000 which is something my computer can't handle.
I'm trying to find the probability distribution of getting a certain value of n dice where no single value of any dice is 1.
For example, with a single dice, the probability of getting a 1,2,3,4,5, or 6 is 1/6.
For two dice, the probability of getting a total value of 4 or 12 is 1/36 (I ignore the case of 2 and 3 since one of the dice has to have a value of 1). The probability of a 5 or 11 WITHOUT a dice having a value of one is 1/18, 6 or 10 WITHOUT a dice having a value of 1 is 1/12, etc. etc.
Is anyone familiar with generating the probability distribution that all the possible values that can be rolled with n dice such that no dice contains a 1?