If two cells are chosen randomly on a 8x8 chessboard what is the probability that they are neighbors (i.e. share a common side)?

There are 64C2 = 2016 ways to choose two random cells.

There are 8*7*2 = 112 ways to choose two adjacent cells (ways to place a 1x2 rectangle).

Then the probability is 112/2016 = 1/18.