I recently discovered a problem similar to this one in a book about Markov chains:
Assume you can buy $n-$ different set of cards in a store, but you do not know which one you'll buy: What is the average number of sets you have to buy until have all $n-$ sets together?
I was really puzzled how this problem can be viewed as a Markov chain? Does anybody have a hint how to solve these kind of problem with markov chains?