How many possible outcomes can you get from rolling two number cubes?

Answer 1

Depends on how many numbers are on each cube. Say one has m numbers and the other has n numbers, you can get mxn outcomes.

* * * * *

This could get rather complicated!

By definition, a cube has only six faces and so each die can have only six numbers on it. BUT, these numbers need not all be different.

If they are all different then m = n = 6 and there are 36 outcomes in all.

More generally, a single die can have

6 outcomes (6 numbers each appearing once)

5 outcomes (4 numbers singly and 1 pair)

4 outcomes (3 numbers singly and 1 triple or 2 singles and 2 pairs)

3 outcomes (2 singles and 1 quartet or 1 single and 1 pair and 1 triple or 3 pairs)

2 outcomes (1 single and 1 quintet or 1 pair and 1 quartet or 2 triplets)

1 outcome (1 sextet).

So m can have any of the six values 1,2,3,4,5,6. And similarly, so can n.

And therefore, m*n can have the following values:

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 12, 15, 16, 18, 18, 20, 24, 25, 30, 36.