[tex]r[/tex] is the number of objects from the total [tex]n[/tex] objects that you want to permute.
For example, if I have the set of characters [tex]\{a,b,c,d\}[/tex], I can choose to permute any of up to 4 of the characters. Suppose I take just 2 of them. Then the formula predicts I should find [tex]{}_4P_2=\dfrac{4!}{(4-2)!}=\dfrac{24}2=12[/tex] possible permutations. Indeed, these are
[tex]\begin{matrix}ab&ac&ad\\ba&bc&bd\\ca&cb&cd\\da&db&dc\end{matrix}[/tex]
