4. Igor Gorshkov has all seven books about Harry Potter. In how many ways can Igor arrange these seven volumes on three different bookshelves, so that each shelf has at least one book? (Arrangements that differ by the order of books on the shelf are considered different).
Answer: $C_{6}^{2} \times 7!=75600$.

Solution: First, we can arrange the books in any order, which gives 7! options. Place two dividers into 6 gaps between the books - this can be done in $C_{6}^{2}$ ways. The dividers will divide the books into three parts, which need to be placed on the 1st, 2nd, and 3rd shelves. In total, we get $C_{6}^{2} \times 7!=75600$ options.