I have different mathematics textbooks and different psychology textbooks. In how many ways can I place the textbooks on a bookshelf, in a row, if there must be a psychology textbook exactly in the middle, and there must be a mathematics textbook at each end?
The 2 Math books at each end can be chosen in: 5C2 ==10 different ways
The psychology book in the middle can be chosen in: 4C1==4 different way
The remaining 6 books (3 math + 3 psychology) can be arranged in: 6! ==720 ways.
Therefore, the 9 books can be arranged in:10 x 4 x 720 ==28,800 ways.