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

question 65

Essay

Provide an appropriate response.
-Consider the following formulas: ${ } _ { n } P _ { r } = \frac { n ! } { ( n - r ) ! }$ and ${ } _ { n } C _ { r } = \frac { n ! } { ( n - r ) ! r ! }$
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 th concept of counting the number of outcomes based on whether or not order is a criterion?