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 $\{ (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,2), (2,3), \dots, (5,6), (6,6) \}$


Here is what is confusing me. Aren't (5,2)(5,2) and (2,5)(2,5) the
  same thing? So we shouldn't really double count?

That assumption is where the issue lies. 5,2 and 2,5 are not exactly the same thing, because the dice aren't physically the same objects. 
Your logic would work if the numbers on the dice were sports teams playing at a fixed stadium, so Team 5 playing Team 2 and Team 2 playing team 5 would be the same game.
But if we introduce the difference in stadiums (i.e. different dice), we get 2 different games: we have Team 5 Playing Team 2 on 5's home stadium (i.e. die #1) and Team 2 Playing Team 5  on 2's home stadium (i.e. die #2)
Another way to think about this is:
How can I get a 2,5 combo? Either first die shows 5 and second shows 2, or the first shows 2 and the other shows 5. Even though both dice are the "same" in terms of appearance, they are not physically the same objects.
How can I get a 3,3, combo? Only one: both dice show 3. (This doesn't really fit in our sports analogy, maybe if a team is practicing with their second-tier side at their home stadium)
So let's say 3,3 has a "probability weight" of 1, while 2,5 has a "probability weight of 2"
Out of your 21 arrangements, 6 are doubles (1,1 2,2 3,3 .. 6,6) which only have a probability weight of 1.
So 15 have a "probability weight" of 2 while 6 have a "probability weight" of 1.
Which gives us 15*2 + 6 = 36 "outcomes".
So for 7, you have 1-6 2-5 3-4 4-3 5-2 6-1 = 6 out of the total 36 "outcomes".
P.S. Another way to think about it is to consider the second die a reroll of the first die. In this case the dice are physically the same, but the order in which you roll a 2,5 matters because "rolling a 5 on my first and a 2 on my second" is different from "rolling a 2 on my first and a 5 on my second".
