A committee of $4$ is to be chosen from $10$ people where order matters for roles (chair, secretary, treasurer, member). Which factorial expression models the number of possible role assignments, and what is the numeric total?

• A. $\frac{4!\cdot 10!}{6!}=120,960$
• B. $10!=3,628,800$
• C. $\frac{10!}{6!}=5,040$
• D. $\frac{10!}{4!\cdot 6!}=210$

Answer: (C)