two squares are choosen at random on a chess board. what is the probability that they have a side in common? Is there any shortcut for this sum

Chess board is divided into 8 X 8 i.e 64 squares.
Total Outcomes (i.e. selecting any 2 squares on chessboard) = 64 C 2
Favourable Outcomes(i.e. selecting 2 squares such that second square chosen has a side common with the first one) :
a) If first square is the corner square.
First square can be selected in 4 C 1 ways. The second square can be then be selected in 2 C 1 ways.

b) If First square lies on one of the edge (but isn't the corner square)
First square can be chosen in 24 C 2 ways. Second square can be chosen in 3 C 1 ways.

c) For any other square chosen as first square
First square can be selected in 36 C 1 ways. Second square can be selected in 4 C 1 ways.

Therefore favourable outcomes = 4 X 2 + 24 X 3 + 36 X 4 = 224
Total outcomes = 64 X 63 / 2 = 1952
Probability = 224 / 1952