How many outcomes are possible if you roll 3 fair dice?

Answer 1

The first cube can land in 6 different ways. For each of those . . .

The second cube can land in 6 different ways. For each of those . . .

The third cube can land in 6 different ways.

All three of them can land in (6 x 6 x 6) = 216different ways.

If the three cubes are different colors, then you can tell the difference among all

of the 216 different possibilities.

But if all three cubes are the same color, then the following 6 different outcomes

all look the same to you:

2-4-6

2-6-4

4-2-6

4-6-2

6-2-4

6-4-2

The number of outcomes that look different to you would be only 216/6 = 36 .