The number of partitions of a set of size $28$ into $7$ disjoint subsets of size $4$

Question

I was wondering if anyone can help with this combinatorics question.

Give, with justification, a simple formula for the number of partitions of a set of size $28$ into $7$ disjoint subsets of size $4$

In an attempt to solve this question I got $$\binom{28}{4,4,4,4,4,4,4} = \frac{28!}{(4!)^7}$$ But not sure if this is correct.

Answer 1

• First you shuffle the $28$ in any of the $28!$ ways.
• Then you can shuffle within each group of $4$ without changing the partition.
• Finally you can shuffle the $7$ groups without affecting the partition.

Hence $$ \frac{28!}{(4!)^7 7!} $$