Source: MIT OCW Course 6.041 / 6.431 Probabilistic Systems Analysis and Applied Probability
Your n guests (n>0) are all baseball fans and they wear baseball caps. There is a total of s teams (s>0) in the league. Everyone of your guests is equally likely to be a fan of any one of these teams.
Compute the expected number of people who will pick a cap from their own team.
The number of caps is also n. You have brought the caps so that if the people behaved in an intelligent manner, each person would have got the cap of his team. The guests already had their team caps and after their arrival they had put their caps in a basket. After the party is over, the guests pick cap randomly from basket.
Update (22 Oct 2010)
Solution posted by Gaurav Sinha (chera) (CSE IITK 1996 Graduate, Now working at Indian Revenue Service) in comments!