Albert is opening a new library. He wants to keep a special rack of books facing the entrance to give the visitors a glimpse of the kinds of books it has. This special rack can hold only 10 books at a time. Every time a new book arrives at the library, he needs to decide whether to add it to the special rack or just place it in one of the regular racks in the library. A book is removed from this rack only if Albert decides to add a new book to it.
He wants to ensure that at any point in time, each book that has ever arrived at the library will be equally likely to be on the special rack. How is he going to do this?