In how many ways can 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.)
+128460
Assuming that there are "n" total people
Anchor Anna and Bob in any two chairs separated by two people.....then the other people can be arranged in (n - 2)! ways
And Anna and Bob themselves can be arranged in 2 ways
So.....the total number of arrangements = 2 * ( n - 2)! ways
