A person wrote letters to \(n\) addressees, one letter in each envelope, and then, at random, wrote one of the \(n\) addresses on each envelope. What is the probability that at least one of the letters reached its destination?

\[ \begin{aligned} P\left\{\sum_{k=1}^{n} A_{k}\right\}=\sum_{i=1}^{n} P\left(A_{j}\right)- & \sum_{1 \leqslant i