Why are the dice outcomes (1, 2) and (2, 1) treated as different outcomes?

In probability theory, the outcomes (1, 2) and (2, 1) are treated as distinct because the two dice are considered identifiable—for instance, by a difference in color.1

When calculating probabilities, we define a sample space consisting of all possible outcomes of an experiment. For two dice, each outcome is represented as an ordered pair (i, j), where i and j correspond to the specific face showing on each individual die. By treating the dice as distinct, we ensure that each of the 36 possible outcomes in the sample space is equally likely. This symmetry is fundamental to calculating the probability of specific events, such as the sum of the faces, by taking the ratio of favorable outcomes to the total number of cases.1