A board has 16 squares as shown in the figure: Out of these 16 squares, two squares are chosen at random. The probability that they have no side in common is :

• A

  7/10
• Correct answer
  B

  4/5
• C

  23/30
• D

  3/5

Solution

$\begin{aligned} & \text { Total }={ }^{16} \mathrm{C}_2 \\ & \text { Required ways }=\text { Total }- \text { (adjacent square) } \\ & ={ }^{16} \mathrm{C}_2- \\ & \text { [3 pair in vertical \& horizontal for } \\ & \text { each row and column] } \\ & ={ }^{16} C_2-[3 \times 4+3 \times 4] \\ & =96 \\ & \text { Probability }=\frac{96}{120}=\frac{4}{5} \end{aligned}$

Hence, the correct answer is option: 'B'.