  We prove the following double inequality related with Burnside's formula for
$n!$ \begin{equation*}
\sqrt{2\pi}\left(\frac{n+a_*}{e}\right)^{n+a_*}<n!<\sqrt{2\pi}\left(\frac{n+a^*}{e}\right)^{n+a^*}\,(n\in\mathbb{N}),
\end{equation*} where the constants $a_*=0.428844044...$ and $a^*=0.5$ are the
best possible. We believe that the method we used in the proof gives insight to
undergraduate students to understand how simple inequalities can be
established.
