The number of ways of throwing n dice each with m faces is
Answer to the Dice Problem
( n + m - 1)! / ( n! * ( m - 1 )! ) where x! is x factorial, i.e., x*(x-1)*(x-2)*...*3.2.1.
Go here for the proof.
So the number of ways of throwing three cubic dice (n = 3, m = 6) is 8!/(3!*5!) = 8*7*6/6 = 56.
Are there more ways of throwing six octagonal dice (n = 6, m = 8) than there are ways of throwing eight cubic dice (n = 8, m = 6)?
One can throw six octagonal dice in 1,716 ways, and eight cubic dice in 1,287 ways (1716/1287 = 4/3).
Mathematical Software Index Home Page