A board has 16 squares as shown in the figure: $\begin{array}{|l|l|l|l|}\hline & & & \\\hline & & & \\\hline…
$\begin{array}{|l|l|l|l|}\hline & & & \\\hline & & & \\\hline & & & \\\hline & & & \\\hline & & & \\\hline\end{array}$
Out of these 16 squares, two squares are chosen at random. The probability that they have no side in common is :
- 7/10
- 4/5
- 23/30
- 3/5
Solution
$\begin{aligned}
& \text {Total }={ }^{16} \mathrm{C}_2 \\ & \text {Required ways }=\text { Total }- \text { (adjacent square) } \\ & \text {[3 pair in vertical \& horizontal for } \\ & \text {each row and column] } \\ & ={ }^{16} C_2-[3 \times 4+3 \times 4] \\ & =96 \\ & \text { Probability }=\frac{96}{120}=\frac{4}{5}
\end{aligned}$ ~
Asked in: JEE Main 2025 (23 Jan Shift 2)