In how many ways can 9 friends sit at a dinner table if two of them, Anna and Bob, insist on having exactly two people seated between them? (As usual, two seatings are considered the same if one is a rotation of the other.)

Anchor Bob and Anna in any of two chairs......and they can be arranged in 2 ways.... [ Bob on Anna's left or right....]

And the other people can be arranged in 7! = 5040 ways

So....the total arrangements are 2 * 7! = 10080 ways