$(5)$ Use combinatorial reasoning to explain why

$(\frac{n}{0})(\frac{n}{n})(\frac{n}{1})(\frac{n}{n-1})(\frac{n}{2})(\frac{n}{n-2})$ cdots $(\frac{n}{n})(\frac{n}{0})=(\frac{2n}{n})$

$($Hint: One example might be a group of $n$ dogs and $n$ cats and you want to choose a group of $n$ animals from among them.$)$