Question 3
Let $n$, $k$ be given positive integers with $n \gt k$. Prove that
$$
\frac{1}{n+1} \cdot \frac{n^{n}}{k^{k}(n-k)^{n-k}} \lt \frac{n!}{k!(n-k)!} \lt \frac{n^{n}}{k^{k}(n-k)^{n-k}}.
$$
$$
\frac{1}{n+1} \cdot \frac{n^{n}}{k^{k}(n-k)^{n-k}} \lt \frac{n!}{k!(n-k)!} \lt \frac{n^{n}}{k^{k}(n-k)^{n-k}}.
$$