2024 AMC 10B Problem 22

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 \qquad \textbf{(B)} 6 \qquad \textbf{(C)} 7 \qquad \textbf{(D)} 8 \qquad \textbf{(E)} 9

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.