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 $\{ (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,2), (2,3), \dots, (5,6), (6,6) \}$
Best Answer
We can perfectly well decide that the outcomes are double $1$, a $1$ and a $2$, double $2$, and so on, as in your proposal. That would give us $21$ different outcomes, not $36$.
However, these $21$ outcomes are not all equally likely. So although they are a legitimate collection of outcomes, they are not easy to work with when we are computing probabilities.
By way of contrast, if we imagine that we are tossing a red die and a blue die, and record as an ordered pair (result on red, result on blue) then, with a fair die fairly tossed, all outcomes are equally likely. Equivalently, we can imagine tossing one die, then the other, and record the results as an ordered pair.
You can compute probabilities using your collection of outcomes, if you keep in mind that for example double $1$ is half as likely as a $1$ and a $2$. The answers will be the same, the computations more messy, and more subject to error.