What is the number of partitions of a set of size $16$ into $4$ subsets of size $4$?

Question

What is the number of partitions of a set of size $16$ into $4$ subsets of size $4$ ?

What I have done:

I have tried ${16 \choose 4} \cdot \frac{{12 \choose 4}}{4!}$ however this gives an answer of $37537.5$ which has a decimal. Am I taking the right approach to this question?

Answer 1

$$\frac{\binom{16}{4}\binom{12}{4}\binom{8}{4}\binom{4}{4}}{{4!}}$$