What's the relationship of $n^n$ and $n!$ complexity with respect to EXPTIME?
$\mathsf{EXPTIME}$ is the class of problems solvable by algorithms whose running time is $O(2^{n^c})$ for some $c&gt;0$. In contrast, $\mathsf{E}$ is the class of problems solvable by algorithms whose running time is $O(2^{cn})$ for some $c&gt;0$.

These definitions show that problems solvable in time $O(n!)$ or $O(n^n)$ are in $\mathsf{EXPTIME}$, but not necessarily in $\mathsf{E}$.