Looking how to calculate (1) the number of permutations for different number ranges on each dice; and (2) the number of permutations for number ranges shared by two or more dice.
All dice are fair and 6 sided.
I can do the easy calculations where how many rolls have exactly one 6, or at least one 6, two 6's, or at least two 6's etc.
'm looking for a more general approach where I have m dice, and find permutations where say where:
at least one die is 5+ and at least another is 4+.
in general I would like to be able to find a formula or counting approach what are the number of permutations where x die are greater than 5, when rolling m dice where a constant c can be distributed across the die.