This question comes from my unsuccessful attempt to solve

http://www.mathhelpforum.com/math-he...-problems.html

(Reason im posting a new thread: dont want to hijack the other one with my own questions).

The question was:

"there are n letters and n addressed envelopes. Letters are placed randomly in envelopes. find the probability that at least 1 letter goes in the correct envelope"

The correct answer is

But i thought it was

So, i have 2 questions:

1) What's the conceptual mistake in my approach

2) Is there a derivation of the subfactorial function somewhere?