$$\begin{array}{|l|l|} \hline \textbf{$m$} & \text{$n=m!$} & \text{$\log n / \log \log n$} \\\hline \text {4} & \text{24} & \text{4/2 = 2} \\ \text {6} & \text{720} & \text{9/3 = 3} \\ \text {8} & \text{720$\times$56} & \text{15/3 = 5} \\ \text {10} & \text{720$\times$56$\times$90} & \text{21/4 = 5} \\\hline \end{array}$$If we see, $m$ is growing at same rate as $ \log n / \log \log n$.
Correct Answer: $A$