I know this is a permutation problem, selecting two from eight. My problem is how to use this information: "must sit one seat away from each other."
In how many ways is it possible to seat eight people at a round table if Alex and Bob must sit one seat away from each other?
Best Answer
Give Alex a choice of the $8$ chairs, then Bob has a choice of $2$ chairs. The remaining guests can arrange themselves in $6!$ ways in the empty chairs left, giving $16\cdot 720 = 11520$ possible arrangements.