How many permutations of $U$ separate $A$ from $B?$
- $2\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2 k) !(k!)^2$
- $\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2 k)!(n!)$
- $n!$
- $\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2 k) !(k !)^2$