I think that you're missing the fact that there's only a 8/9 chance that you're not selected as the first of the other positions (say, secretary), so the odds are really:

9/10 chance not president
1/9 chance secretary
8/9 chance not secretary * 1/8 chance that, then, you become treasurer

So a 1/9 * 9/10 chance of being secretary, or 1/10

Then a 9/10 * 8/9 * 1/8 chance that you become treasurer

That would be 1/10 + 1/10 = 2/10. Is that the right answer? It almost seems too easy when you look at it like that, but I think that was your mistake before, so this at least accounts for that.

Thats right but how do you know what order to apply the fractions any order works?

Well if you're multiplying the order shouldn't matter (is that the transitive property? I know there's a name for it from school), so as long as you're setting it up right you should be okay. Glad that was right! I thought I might have missed something but at least thought that I could see where the first mistake was.