How to give a combinatorial proof for: If $n$ and $k$ are positive integers with $n=2k$ then $\frac{n!}{2^k}$ is an integer How can i give a combinatorial proof for if $n$ and $k$ are positive integers with $n=2k$ then $\dfrac{n!}{2^k}$ is an integer?

If $n=2k$, $\dfrac{n!}{2^k}$ can be written as the multinomial $\dbinom{n}{2,\dots,2}$ (with $k$ $2$'s), and is therefore an integer.
