The number of ways of selecting two 1 × 1 squares from a chess board such that they

Consider square of 2 × 2, in which we have 2 pairs of
squares which have common vertex.
We have such 7 × 7squares of size 2 × 2.
So, number of ways of selecting two squares having
one vertex common is 7 × 7 × 2 = 98
In each row or column we have 7 pairs of squares
having one side common.
So, number of ways of selecting two squares having
one side common is 7 × 8× 2 = 112.
Therefore, number of ways of selecting two squares
such that they neither have a common vertex nor
have a common side is ${ }^{64}{\mathrm{C}}_2-98-112=1806$