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?
Answer Choices:
A.
B.
C.
D.
E.
💬 Join the Discussion
Stuck on this problem or want to share your approach?
Continue the conversation and see what others are thinking: View Forum Thread
Without loss of generality, suppose the tallest athletes draw first. The condition is equivalent to saying they must all draw different colored wristbands. Regardless of which color band the first person draws, the second person has a chance to draw a different colored band on their draw. The third person then has a chance to draw a band different from the other two. Thus the final answer is
The problems on this page are the property of the MAA's American Mathematics Competitions