AMC 12 2024b Problem 16

A group of $16$ people will be partitioned into $4$ indistinguishable $4$-person committees. Each committee will have one chairperson and one secretary. The number of different ways to make these assignments can be written as $3^{r}M$, where $r$ and $M$ are positive integers and $M$ is not divisible by $3$. What is $r$?

$\textbf{(A) }5 \textbf{(B) }6 \textbf{(C) }7 \textbf{(D) }8 \textbf{(E) }9$