Difference between 2 dice rolls

#1
Hey all,
I encountered a problem thats been puzzling me in my quantum physics class today and I couldn't get a good statistical answer from my professor. While we were looking at probability we ran a short experiment where we rolled 2 dice and recorded the difference between their outcomes (ie one rolled 6 and another 2 the difference is 4). When looking at theoretical outcomes you can make a table like the attached image. My problem is why is the roll (1,2) different than the roll (2,1) but we dont count (1,1) differently than the oppositely ordered (1,1)? If we double count the extra (1,1),(2,2) ... we come up with an x/42 chance instead of x/36 like it should be. If someone could explain to me why (2,1) and (1,2) creates an extra probability than (1,1) and (1,1) I'd appreciate it greatly.
Thanks! -Alex dice.PNG
 
#2
Think about it in terms of rolling one die twice. There is only one way to roll a 1 on the first and a 1 on the second. But i can roll a 2 and then a 1 or a 1 and then a 2. The other way to think about it is the dice are indistinguishable.