Finding the limit $\lim_{n\to \infty}\frac{n^k}{n\choose k}$ I am confused with solving problems with combinatorial limits. My question here is that for $k\in N$, what is the $$\lim_{n\to \infty}\frac{n^k}{n\choose k}$$

Note that:
As n $\to \infty$,
$$\frac{n^{k}}{\binom{n}{k}}=\frac{n^{k} k!}{n(n-1)(n-2)\cdot\ldots \cdot(n-k+1)}=\frac{k!}{1\cdot\left(1-\frac{1}n\right)\left(1-\frac{2}n\right)\cdot\ldots\cdot\left(1-\frac{k-1}{n}\right)} \to k! $$
