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?
Right now I have the total number to deliver two letters to $n$ houses as $N = \frac{(2n)!}{2^n}$.
I know derangement is equal to $N - N_1 + N_2 - N_3 + ... + (-1)^kN_k$.
I have $N_1 =\displaystyle{n \choose 1}\bigg[\frac{(2n-2)!}{2^{(n-1)}}\bigg]$ but I can't seem to find a pattern or find a solution.
