Question

Two squares of a chess board having 64 squares are selected at random the probability that they have a side in common is

• A. $\frac{56}{64C_2}$
• B. $\frac{112}{64C_2}$
• C. $\frac{168}{64C_2}$
• D. $\frac{268}{64C_2}$

Answer 1

The correct option is B $\frac{112}{64C_2}$

In a $8\times 8$ chessboard, along a particular row, there can be $7$ sides common. This, counted across $8$ rows gives $56$ possible cases. The same thing can happen across $8$ columns resulting in $56$ possible cases.
Therefore, possible cases = $56+56=112$
Hence, probability = $\frac{112}{{}^{64}{C}_2}$