Is the OP still confused by this?

I think he’s mixing up two different questions:

Suppose the three dice are three different colors.

And suppose you are asked: How many ways could you roll one 5 and two 6’s?

```
Red Blue Green
--- ---- -----
5 6 6
6 5 6
6 6 5
```

In this counting, it matters what numbers come up on which colored cubie. So there are three ways.

But if the dice are all the same color, they all look alike. You MIGHT say that there is only one way.

But you might, instead, distinguish the three dice by “first one”, “second one”, and “third one”. Or “the one on the left”, “the one in the middle”, and “the one on the right”.

Moral of the story: You need to be very sure exactly what the question is!

In general, you always need to know which of these questions you are being asked: If the order of the individual dice matters, or if the order doesn’t matter.

When you are adding up the probabilities, you need to treat them as if the order matters. (Or, as if the dice are different colors. Or as if you distinguish “first rolled”, “second rolled”, “third rolled”.) If the dice are all one color, then the three possibilities in the table above look all alike, but there are still three times as many chances for 17 to come up, just as if they were different colors.