2025 AMC 10B Problem 11

On Monday, 6 students went to the tutoring center at the same time, and each one was randomly assigned to one of the 6 tutors on duty. On Tuesday, the same 6 students showed up, the same 6 tutors were on duty, and the students were again randomly assigned to the tutors. What is the probability that exactly 2 students met with the same tutor both Monday and Tuesday?

\textbf{(A)} \dfrac{1}{16} \qquad \textbf{(B)} \dfrac{3}{16} \qquad \textbf{(C)} \dfrac{1}{4} \qquad \textbf{(D)} \dfrac{3}{8} \qquad \textbf{(E)} \dfrac{1}{2}

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