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?

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The Answer of 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?

Provide an Appropriate Response nPr=n ! (n−r)!{ }_{n} \mathrm{P}_{\mathrm{r}}=\frac{\mathrm{n} \text { ! }}{(n-r) !}n​Pr​=(n−r)!n ! ​

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