Let $a_n=\large\frac{10^n}{n !}$ for $n=1,2,3.......$ Then the greatest value of $n$ for which $a_n$ is the greatest is :

Question

$$\begin {array} {1 1} (1)\;11 & \quad (2)\;20 \\ (3)\;10 & \quad (4)\;8 \end {array}$$