Find the range of the function $f(r) =$ $^{7-r}P_{r-3}$ where $^m P_n$ is the number of permutations of $n$ objects from $m$ objects (given that $r>0$) .
What I Tried :- I am really not that familiar with the definition of range of a function, but here's what I did :-
If $f(r) =$ $^{7-r}P_{r-3}$ , then $(7 - r) > 0$ , $(r - 3) > 0$, since as far as I know $m!$ is not defined if $m < 0$. This gives that $r < 7$, $r > 3$ . So $r$ is maximum $6$ and minimum $4$ in terms of integers.
I checked the definition of the range of a function, and it says that the range of a function is the set of all output values derived from that function. So as far as my point of view, the answer is {$^3 P_1$ ,$^2 P_2$ ,}
Can someone confirm this for me? If not, can anyone show me how to do this problem?