Suppose that I have \(6\) different books, \(2\) of which are math books. In how many ways can I stack my \(6\) books on a shelf if I do not want the math books to be next to each other?
Total arrangements - The number of arrangements where the ARE together
The can be together in 5 ways and for each of these they can be arranged in 2 ways
6! - 2 * 5 =
6! - 10
720 - 10 =