I have 5 different biology textbooks and 4 different economics textbooks. In how many ways can I place the 9 textbooks on a bookshelf, in a row, if there must be an economics textbook in the middle, and there must be a biology textbook at each end?
1440 and 172800 are wrong
There are 9 ways to choose the economics textbook in the middle, then 5*4/2 = 10 ways to choose the biology textbooks at the end. There then 3! ways to arrange the left textbooks, and 3! ways to arrange the right textbooks, so there are 9*10*6*6 = 3240 ways of arranging the textbooks.