Q:

Fundamental principale of permutations

I have just begin to learn about Permutation and combination. (Just learned definition and factorial.)
In which i have learn: $\sideset{_n}{_r}P=n(n-1)(n+1) \dots (n-r+1)$, $r\le n$ where $n=$distinct object that can be arranged in a line and $r=$nuber of time n object can be arranged. 
My question what if $r\ > n$? 
I know we can't use Permutation there but is there any other thing we can use?

A:

First of all what are you looking for is called $k$-permutations of $n$, or I think a better – but a little bit oldish name for it – variation.
Furthermore your question is what about if $r>n$ because the $r=n$ case is handled by the definition what you have written almost correctly.
Almost, because the correct definiton is:
$$\sideset{_n}{_r}P = \begin{cases} \frac{n!}{(n-r)!} = n(n-1)(n+1) \dots (n-r+1), & \mbox{if } r \leq n \\  0,  & \mbox{otherwise.} \end{cases}$$
Of course there are a lot of properties and identities for it, because it is a very fundamental tool in mathematics. You can find interpretations aswell. Maybe you could start with Permutation wikipedia article.

