2025 AMC 10A Problem 14

Six chairs are arranged around a round table. Two students and two teachers randomly select four of the chairs to sit in. What is the probability that the two students will sit in two adjacent chairs and the two teachers will also sit in two adjacent chairs?

\textbf{(A)} \dfrac{1}{6} \qquad \textbf{(B)} \dfrac{1}{5} \qquad \textbf{(C)} \dfrac{2}{9} \qquad \textbf{(D)} \dfrac{3}{13} \qquad \textbf{(E)} \dfrac{1}{4}

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