AMC 10B 2025 (Problem 11)

CombinatoricsHard

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?

\text{(A)}\;\frac{1}{16}

\text{(B)}\;\frac{3}{16}

\text{(C)}\;\frac{1}{4}

\text{(D)}\;\frac{3}{8}

\text{(E)}\;\frac{1}{2}