Consider the following formulas: $${ } _ { n } \mathrm { P } _ { \mathrm { r } } = \frac { \mathrm { n } ! } { ( \mathrm { n } - \mathrm { r } ) ! } \text { and } \mathrm { n } _ { \mathrm { r } } = \frac { \mathrm { n } ! } { ( \mathrm { n } - \mathrm { r } ) ! \mathrm { r } ! }$$ 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?

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The Answer of Consider the following formulas: $${ } _ { n } \mathrm { P } _ { \mathrm { r } } = \frac { \mathrm { n } ! } { ( \mathrm { n } - \mathrm { r } ) ! } \text { and } \mathrm { n } _ { \mathrm { r } } = \frac { \mathrm { n } ! } { ( \mathrm { n } - \mathrm { r } ) ! \mathrm { r } ! }$$ 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?

Consider the Following Formulas Given the Same Values for N and R in Each