group combinations - pairing

[ssmmss]

Hello,

If we have n students in a classroom. We want to assign the students a group final project. If the teacher wants the students to pair into groups of 3, how many ways are there to choose the groups in which the order doesn’t matter.

My answer is: (n!)/((n-3)! . 3!)

 

[pka]

If we have n students in a classroom. We want to assign the students a group final project. If the teacher wants the students to pair into groups of 3, how many ways are there to choose the groups in which the order doesn’t matter.

My answer is: (n!)/((n-3)! . 3!)

This is an poorly worded question.
First we need to know that \(\displaystyle n=3k\) That is a multiple of three.
The words "to pair" is confusing. I take it to mean "to group" or "to assign".

Answer: \(\displaystyle \dfrac{n!}{(3!)^k(k!)}\)