Just an imagination

Method 1: We can write the given expression as ${_0P_r}$ i.e. ${0 \choose r}*r!$ . Now, if we write ${0 \choose r}$ , it means number of ways to select 'something' from 'nothing' . Since there is no way to perform this task ; implies that ${0 \choose r}=0$ Hence ${_0P_r}=0 \Rightarrow \frac { 1 }{ (-r)!} =\boxed { 0 }$

Method 2 : We can write $r!=r(r-1)!$ . If we write it for $r=0$ , it will be $0!=0(-1)!$ which gives $(-1)!=1/0=\infty$ . If we go to generalise it, we can write it as $(-r)!={ \left( -1 \right) }^{ r+1 }\infty$ therefore our expression becomes $\frac { 1 }{ { \left( -1 \right) }^{ r+1 }\infty } =\boxed { 0 }$