AMC 10B/12B 2025 (Problem 14/11)
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 blue bands, red bands, and 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?
There are ways to assign three blue bands to players and so on.
Favorable:
WLOG, suppose the first person is taller than the second person and so on.
The 1st, 2nd, and 3rd persons should draw different colors
2 blue bands are left ways to assign them to two players.
WLOG, suppose the first person is taller than the second person and so on.
The 1st, 2nd, and 3rd persons should draw different colors
2 blue bands are left ways to assign them to two players.
(C)