2 problems

Let $\mathcal{S}_k$ denote the permutations of $[k]$. Fix $\varepsilon>0$ and set $n=(1+\varepsilon)k^2/4$. For $\pi\in\mathcal{S}_k$, let $\sigma$ be a uniformly random permutatio…

Let $k$ be a positive integer. Let $\pi$ be a permutation of length $k$, let $n=1000k^2$, and let $\sigma$ be a uniformly random permutation of length $n$. Containment probability…