Given the Same Values for N and R in Each

Essay

$\text { Consider the following formulas: } ( n ) _ { r } = \frac { n ! } { ( n - r ) ! } \text { and } \left( \begin{array} { l } n \\ r \end{array} \right) = \frac { n ! } { ( n - r ) ! r ! } \text {. }$
Given the same values for n and r in each formula, which is the smaller value, P or C? How does this relate to the concept of counting the number of outcomes based on whether or not order is a criterion?