Question 4
Let $n,k$ be positive integers with $n\gt k$. Prove that
$$\frac1{n+1}\frac{n^n}{k^k(n-k)^{n-k}}\lt \frac{n!}{k!(n-k)!}\lt \frac{n^n}{k^k(n-k)^{n-k}}.$$
$$\frac1{n+1}\frac{n^n}{k^k(n-k)^{n-k}}\lt \frac{n!}{k!(n-k)!}\lt \frac{n^n}{k^k(n-k)^{n-k}}.$$