I have $4$ different mathematics textbooks and $3$ different psychology textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if there must be a mathematics textbook exactly in the middle, and all the psychology textbooks are together?

tomtom Dec 29, 2023

#1**+1 **

If all the psychology books are together, then so are all the mathematics textbooks

The books can be arranged in two ways (psychology first and then math, or vice-versa)

And for each of these the math books can be arranged in 4! = 24 ways

And the psychology books can be arranged in 3! = 6 ways

So

6 * 24 * 6 = 864 arrangements

CPhill Dec 29, 2023