How many possible outcomes are from tossing two cubes labelled 1 through 6?

Answer 1

As each cube can land with 1 of 6 faces on top there are 6 × 6 = 36 possible outcomes

If the numbers displayed on the top faces are added together then there are 11 possible outcomes: 2, 3, 4, ..., 11, though they do not all occur with the same frequency:

2 can only occur when both cubes show a 1

3 can occur when one shows a 1 and the other shows a 2

4 can occur when one shows a 1 and the other shows a 3, or they both show a 2

and so on.

The number of ways the sums can occur is:

2 - 1 way

3 - 2 ways

4 - 3 ways

5 - 4 ways

6 - 5 ways

7 - 6 ways

8 - 5 ways

9 - 4 ways

10 - 3 ways

11 - 2 ways

12 - 1 way

1 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1 = 36 - all the possible outcomes of throwing the two cubes.

Answer 2

There are 36 outcomes.