An exercise for the student
I'm a creature of habit. There are a lot of areas in which I don't like trying new things, especially if I've already found something that I already really like. This is particularly true when it comes to music; in fact, I pretty much dislike every song I hear, the first time I hear it. (There have been some exceptions, but then sometimes I got sick of those songs really easily.)
As you might imagine, this makes finding new music to listen to rather tricky. However, I've discovered that if I buy an album which has a few songs on it that I already know and like, I can generally suffer through listening to the rest of them until I actually start liking them, as well.
I used to buy a new CD ever time I had to make a cross country trip, and then I'd put the CD on shuffle until I'd heard all of the songs I liked. (Then I'd typically take it out and put in an old favorite.)
Which brings us to our exercise.
Given a CD with m songs I like on it and n total tracks (where we assume that n ≥ m), how many songs will I have to listen to on average before I hear all of the songs that I like? (Remember that the CD player is on shuffle, not random, so each track will play exactly once before any of them repeat.)
I once derived a general solution to this, which I'll add as a comment, but I don't understand why it works, only that it does. (For low values of m and n, at least. Katya's Last Theorem, anyone?)