I have 5 different mathematics textbooks and 2 different psychology textbooks. In how many ways can I place the 9 textbooks on a bookshelf, in a row, if there must be a mathematics textbook in the middle?
Guest, I assume you mean how many ways you can put 7 textbooks on the bookshelf .
If this is true, we can use some simple counting to solve this. We know that this bookshelf has to be of the form
_ _ _ M _ _ _
if M is a math textbook. So we simply need to find ways to arrange the other textbooks. We know all of the textbooks are different from the problem, so we do not have to worry about distinguishability. Thus, there are \(6! = 720\) ways of arrangement.