$18$ mice were placed in $3$ groups, with all groups equally large. In how many ways can the mice be placed into $3$ groups?

Question

In my textbook, the given answer is $18!/(6!)^3$.

But my teacher's answer is $18!/(3!)(6!)^3$. He solved like -

Please review the attached answer and let me know which one answer is correct? Thank in advance!

Answer 1

It depends if groups are distinguishable. For e.g. if you put 6 mouse each in 3 different color boxes then your textbook is correct, if you put them in same color boxes then your teacher is correct.

Take a smaller case say 4 mouse and 2 boxes and then think about. You might want to write down all the possibilities to give you clarity.

Ans clearly mentions in the way textbook has treated order in which groups are formed matter (i.e. they are distinguishable you can label them 1,2,3)