2025 AMC 10B Problem 14

Nine athletes, no two of whom are the same height, try out for the basketball team. One at a time, they draw a wristband at random, without replacement, from a bag containing 3 blue bands, 3 red bands, and 3 green bands. They are divided into a blue group, a red group, and a green group. The tallest member of each group is named the group captain. What is the probability that the group captains are the three tallest athletes?

\textbf{(A)} \dfrac{2}{9} \qquad \textbf{(B)} \dfrac{2}{7} \qquad \textbf{(C)} \dfrac{9}{28} \qquad \textbf{(D)} \dfrac{1}{3} \qquad \textbf{(E)} \dfrac{3}{8}

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