Problem:
The nine delegates to the Economic Cooperation Conference include officials from Mexico, officials from Canada, and officials from the United States. During the opening session, three of the delegates fall asleep. Assuming that the three sleepers were determined randomly, the probability that exactly two of the sleepers are from the same country is , where and are relatively prime positive integers. Find .
Solution:
There are equally likely ways to select the three delegates who fall asleep. There are ways to select them so that exactly two delegates are from the United States, ways to select them so that exactly two delegates are from Canada, and ways to select them so that exactly two delegates are from Mexico. The desired probability is therefore . The requested sum is .
The problems on this page are the property of the MAA's American Mathematics Competitions