Number of combinations with given outcomes for a set number of dice rollsHow to find...
Number of combinations with given outcomes for a set number of dice rolls
How to find the number of combinations for n rolls of a pair of 6-sided dice with all of the specified sums rolled at least once?
Example. A pair of 6-sided dice is rolled 5 times. What is the number of combinations containing each of: 3, 4, 8 at least once? So that (3, 7, 8, 5, 4) is counted and (3, 4, 2, 2, 12) is not.
Thoughts on the example. It's possible to roll 3 in 2 ways, 4 in 3 and 8 in 5 and the total number of outcomes is 36. So I think the number of combinations containing 3, 4, 8 is:
Where D is duplicates. But if this is correct, not sure what pattern the duplicates follow.