There are two indistinguishable dice. How many different outcomes are possible?

If the dice are indistinguishable, then the order of the outcomes does not matter. Each die has 6 faces, so there are 6×6=36 possible outcomes considering order. But since the dice are identical, pairs (1,2) and (2,1) are considered the same outcome.

The number of distinct outcomes is the number of combinations with repetition from 6 taken 2 at a time:

[ C = \frac{6 \times (6 + 1)}{2} = 21 ]

That is, there are 21 unique outcomes when rolling two indistinguishable dice.