Probability of getting a certain sum of two dice; confusion about order If you roll two six-sided dice, the probability of obtaining a $7$ (as a sum) is $6/36$.
Here is what is confusing me. Aren't $(5,2)$ and $(2,5)$ the same thing? So we shouldn't really double count?
Thus by that logic, wouldn't the actual answer be $3/21$ instead?
EDIT: My $21$ possibilities came from $\{ (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,2), (2,3), \dots, (5,6), (6,6) \}$

The problem with that logic is that the 36 possible options take into account treating the dice as individual rolls. There are indeed fewer than 36 possible outcomes if you just consider pairings of the dice, but that isn't where the probability of the rolls come from. The probability comes from allowing each die to vary individually, and the fact that one of the dice rolling a two doesn't exclude the chance that the other die could still roll a five and the sum would be seven, the same being true for the first die rolling a five not excluding the chance of the second rolling a two. So we take this into account by paying attention to both possibilities when count the possible outcomes.
