Question: n letters belong to n envelopes. How many ways can these be arranged such that each letter is in the wrong envelope?
I'm quite stuck. I was thinking of applying the Inclusion-Exclusion Principle, so taking:
(Total combinations = n!) - |A1 u A2 u ... u An|, where Ai is the set where i letters are in the correct envelope.
I'm not sure if that's the correct method, but even if it is, I'm not sure what to write as the final answer?
Thanks for any help