What is the probability of getting double dice? (one throw)
All possible dice rolls are 36 (counting even rolls like 1-4 and 4-1).
But when counting the doubles, why not count 1-1 twice, for example?
My book says the probability is 6/36.
You don't count (1,1) twice, because the situation "both dice show a 1" can only occur in one way - the first dice is 1, and the second dice is 1.
By contrast, the situation "one dice shows a 4, the other shows a 1" can occur in two ways - either the first dice is 4 and the second is 1, or the first dice is 1 and the second is 4.
The easiest way to convince yourself of this is to tabulate all 36 possibilities:
Before you roll your dice, colur one of them red and the other blue. Then red $1$ and blue $1$ is the same thing as blue $1$ and red $1$.
But red $1$ and blue $5$ is not the same as blue $1$ and red $5$.