Provide an Appropriate Response ${ }_{n} \mathrm{P}_{\mathrm{r}}=\frac{\mathrm{n} \text { ! }}{(n-r) !}$

Essay

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