Two squares are chosen at random on a chess board. The probability that they have a side in common is

n(S) =64C2= 32×63  the number of ways of selecting two sqaures for which one side is common in a row is → 7 ways   For 8 rows→ 7×8 = 56 ways   Similarly  for 8 columns =  56 ways ∴ n(E) = 56+56 = 112P(E) = 2×5632×63 = 118 .