you can do this with a tree diagram, where each branch has 2 possible outcome (correct, not correct).

I wouldn't try and draw the whole thing, but its good to ahve in the back of your head.

Step 1:

Find the probability that no paycheck is in the correct envelope:

P(0) =

Step 2:

P(at least 1) = 1-P(0)

Check for n=3:

, which you said was correct