Sorry if this seems trivial. I'm starting to think I'm pretty stupid for not understanding such a simple problem.
There are no other restrictions. An advisor may get multiple students, but one student may not get multiple advisors.
I approached this by drawing $5$ slots corresponding to advisors and figuring out how many students can be assigned, without repetition (i.e. once a student gets assigned, they are no longer reused):
[24] x [23] x [22] x [21] x [20] = $P(24, 5)$
The book says that I should actually be treating the students as the slots and assigning instructors:
[5] x [5] x [5] x [5] x …. = $5^{24}$
Why is my logic wrong?
Best Answer
Your approach only assigns one student to each adviser. The other $19$ students do not get an adviser at all. The question asks you to send each student to an adviser, with the possibility that one adviser gets all the students. They are two very different questions with very different answers.