Question

How many ways are there to assign \({\rm{24}}\) students to five faculty advisors?

Short answer

There are \({\rm{59,604,644,775,390,625}}\)ways to assign \({\rm{24}}\)students to five faculty advisors.

Step-by-step solution

Introduction

In mathematics, a permutation of a set is a loose organization of its members into a sequence or linear order, or a rearrangement of its elements if the set is already sorted. The act or process of altering the linear order of an ordered set is often referred to as "permutation."

Explanation

Wemustapplythepermutationideasincetheorderoftheadvisersiscrucial(becauseadifferentorderresultsincertainstudentshavingdifferentadvisors).

As mentors, we'd want to pair \({\rm{24}}\) students with five professors.

\(\begin{array}{l}{\rm{n = 5}}\\{\rm{r = 24}}\end{array}\)

Since repetition is allowed:

\({{\rm{n}}^{\rm{r}}}{\rm{ = }}{{\rm{5}}^{{\rm{24}}}}{\rm{ = 59,604,644,775,390,625}}\).

Therefore, there are \({\rm{59,604,644,775,390,625}}\)ways to assign \({\rm{24}}\)students to five faculty advisors.