Question

In how many ways can Ann, Bob, Chuck, Don and Ed be seated in a row such that Ann and Bob are not seated next to each other?

Answer 1

the direct answer with not much explanation is
\[5!-2\times 4!\]

Answer 2

the explanation is that if there were no restrictions it would be \(5!\)
the number of ways that they can be seated together:
treat them as one unit, you get \(4!\) but we need to count AB different from BA so that is why it is \(2\times 4!\)