Fixed Point Probability in a Random Permutation
Pick a uniformly random permutation $f: [n] \rightarrow [n]$, where $[n] = \{1, 2, \ldots, n\}$. We call index $i$ a fixed point if $f(i) = i$ -- it maps to itself.
With $n = 10$, what is the probability that
$ is a fixed point but
$ is not?Open the full interactive solver, hints, and worked solution →