Two dice are rolled. What is the probability that the sum of the numbers on the dice is at least 10
Let $Z$ denote the set of successful outcomes:
$Z=\{(4,6),(6,4),(5,5),(5,6),(6,5),(6,6)\}\\ \text{Sample space: } S=6^2$
So the answer gives the probability as, $P=\frac{6}{36}$.
My question is why are the pairs $(5,5),(6,6)$ only included once? The way I see it for two dice $D_1,D_2$ is it may appear as $D_1: 5,D_2: 5$ or $D_2: 5,D_1: 5$, so why don't we count for this as two outcomes?