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

$n\left(S\right)={64}_{C_2}=32\times 63$ 

$the number of ways of selecting two sqaures for which one side is common in a row is \to 7ways$  

$For8rows\to 7\times 8=56ways$  

Similarly  $for8columns=56ways$

$\therefore n\left(E\right)=56+56=112$

$P\left(E\right)=\frac{2\times 56}{32\times 63}=\frac{1}{18}$ .