I have 7 different geometry textbooks and 4 different algebra textbooks. In how many ways can I place the 11 textbooks on a bookshelf, in a row, if there must be an algebra textbook in the middle, and there must be a geometry textbook at each end?
There are 7 ways to choose the geometry textbook at one end, then 6 ways to choose the geometry textbook at the other end. Then there are 9 ways to choose the second textbook, 8 ways to choose the third textbook, and so on. But then there are 4 ways to choose the algebra textbook, so there are 7*6*9!*4 = 60963840 ways that work.
