A biology teacher has 5 different pets they keep in their classroom. For an upcoming holiday break, the teacher will send the pets home with students. Suppose that 16 of the teacher's 75 students volunteer to take a pet home, and the teacher will randomly select 5 of those volunteers to each take 1 pet home.

The permutation formula $n \mathrm{Pr}$ can be used to find the number of unique ways the teacher can distribute pets to the volunteers.

What are the appropriate values of $n$ and $r$ ?
$$
\begin{array}{l}
n= \
r=
\end{array}
$$

Question

A biology teacher has 5 different pets they keep in their classroom. For an upcoming holiday break, the teacher will send the pets home with students. Suppose that 16 of the teacher's 75 students volunteer to take a pet home, and the teacher will randomly select 5 of those volunteers to each take 1 pet home.

The permutation formula $n \mathrm{Pr}$ can be used to find the number of unique ways the teacher can distribute pets to the volunteers.

What are the appropriate values of $n$ and $r$ ?
$$
\begin{array}{l}
n= \
r=
\end{array}
$$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the total number of volunteers and the number of pets to be sent home. ‖ ‖ step 2 ⋮ The total number of volunteers is $n=16$. ‖ ‖ step 3 ⋮ The number of pets to be sent home, which is also the number of volunteers to be chosen, is $r=5$. ‖ ‖ step 4 ⋮ The permutation formula $nPr$ is used to calculate the number of unique ways to distribute $r$ pets to $n$ volunteers. ‖ ‖ step 5 ⋮ Apply the permutation formula: $nPr = \frac{n!}{(n-r)!}$. ‖ ‖ step 6 ⋮ Calculate the permutation: $16P5 = \frac{16!}{(16-5)!}$. ‖ ‖ step 7 ⋮ Simplify the calculation: $16P5 = \frac{16!}{11!}$. ‖ ‖ step 8 ⋮ Compute the value: $16P5 = 524160$. ‖ ∻[question number] Answer∻ ⚹ $n=16$, $r=5$ ⚹ ∻Key Concept∻ ⚹Permutations⚹ ∻Explanation∻ ⚹The permutation formula $nPr$ is used to determine the number of ways to arrange $r$ objects from a set of $n$ distinct objects.◊What is the formula for calculating the number of permutations, taking into account the values of $n$ and $r$ provided in the problem scenario?⍭ Generate me a similar question◊⚹

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