Question About Probabilities

[Q.E.D.]

I have a problem that keeps coming up that seems basic but I can't figure out. There are some circumstances where you account for different combinations of possible outcomes and some where you don't and I can't figure out what separates the two situations.

For example, say you have AA in holdem and you want to know the probability of flopping exactly one ace and the probability of flopping no aces.

For exactly one ace you have Axx, xAx, xxA flops where x are non ace cards, or (( 2 x 48 x 47 )/ ( 50 x 49 x 48 )) x 3 combinations.

For no aces you have (48 x 47 x 46) / (50 x 49 x 48) and don't have to consider possible combinations.

This seems pretty basic but I'm constantly coming across situations where I'm not sure if I need to account for combinations. What's the determining factor?

Thanks