upper and lower bounds to binomial coefficient

Given two integers $n,k>0$ such that $k\\leq n$ , we have the following inequalities for the binomial coefficient ${n\\choose k}$ :

$\\displaystyle{n\\choose k}$	$\\displaystyle\\leq$	$\\displaystyle\\frac{n^{k}}{k!}$
$\\displaystyle{n\\choose k}$	$\\displaystyle\\leq$	$\\displaystyle\\left(\\frac{n\\cdot e}{k}\\right)^{k}$
$\\displaystyle{n\\choose k}$	$\\displaystyle\\geq$	$\\displaystyle\\left(\\frac{n}{k}\\right)^{k}$

Here $e$ is the base of natural logarithms.Also, for large $n$ , ${n\\choose k}\\approx\\frac{n^{k}}{k!}$ .