Two letters need to be delivered to each of n houses. How many ways can a postman deliver two letters to each house such that each house receives at least one incorrect letter?
I got stuck and don't now how to progress. Can someone provide hint?
1) $(2n)!/2^n$ is the number of all possible onto functions from our domain of houses to the codomain of letters.
2) Let $A_i$ be property that two delivered letters are correct. $ |A_1' \cup A_2' \cup... \cup A_n'|=(2n)!/2^n-|A_1 \cap A_2 \cap... \cap A_n|$ I tried everything I could come up with but I cannot find $|A_1 \cap A_2 \cap... \cap A_n|$. I feel like I need to find union first but in order to do that I should find intersection. Really confused. Any hint would be appreciated.
Edit: Corrected mistake in the equation.