Xavier Aptitude Test 2023 Paper

From the given information, we get that it is 8 inch $\times 8$ inch square grid.Total ways of selecting 2 squares out of 64 in ${}^{64}{\mathit{C}}_2$.
Two squares with a common side can be selected in the following ways.
(i) Horizontal Pairs.
In the first row, R1, we can select 7 pairs of squares with a common side.
They are (R1C1,R1C2), (R1C2,R1C3),.....(R1C7,R1C8).
It applies to other rows as well.
Hence the total number of squares $=7\times 8=56$
(ii) Vertical Pairs.
In the first column, C 1 , we can select 7 pairs of squares with a common side.
They are (R1C1,R2C1), (R2C1,R3C1),....(R7C1,R8C1).
It applies to other columns as well.
Hence the total number of squares $=7\times 8=56$
The probability of two painted squares having a common side $=\frac{56+56}{{}^{64}{\mathit{C}}_2}=\frac{112}{2016}$. Option (A) is correct.