  We prove that the sequence $n!\,(\bmod\,p)$ occupies at least
$\sqrt{\frac{3}{2}N}$ residue classes in the short interval $H\le n \le H+N$
and $N\gg p^{\frac{1}{4}}$ improving previously known trivial bound $\sqrt{N}.$
In the other direction, we estimate the average number of residue classes
missed by the sequence $n!\,(\bmod\,p)$ for $p\le x.$
