Câu hỏi 3
Cho các số nguyên dương $n$, $k$ với $n\gt k$. Chứng minh rằng
$$
\frac{1}{n+1}\cdot\frac{n^{n}}{k^{k}(n-k)^{n-k}}\lt \frac{n!}{k!(n-k)!}\lt \frac{n^{n}}{k^{k}(n-k)^{n-k}}.
$$
$$
\frac{1}{n+1}\cdot\frac{n^{n}}{k^{k}(n-k)^{n-k}}\lt \frac{n!}{k!(n-k)!}\lt \frac{n^{n}}{k^{k}(n-k)^{n-k}}.
$$