MathNet 2025 — Part 01 (100 complete bilingual questions) Question 80

Let $f:\{1,2,3,\ldots ,9\} \to \{1,2,3,\ldots ,9\}$ be a permutation chosen uniformly at random from the $9!$ possible permutations. Compute the expected value of $\underbrace{f(f(\cdots f(f(1))\cdots))}_{2025\ f\ s}$.