QJEEM25Ma5e21: JEE Main 2025 Mathematics - Class 12 JEEM25Ma5e21 Solution: A board has 16 squares as shown in the figure : Out of these 16 …

Question

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A board has 16 squares as shown in the figure :

JEE Main 2025 (Online) 23rd January Evening Shift Mathematics - Probability Question 5 English

Out of these 16 squares, two squares are chosen at random. The probability that they have no side in common is :

Accepted Answer

Total ways for selecting any two squares $={ }^{16} \mathrm{C}_2=120$

Total ways for selecting common side squares

JEE Main 2025 (Online) 23rd January Evening Shift Mathematics - Probability Question 5 English Explanation

$\begin{aligned} = 24 \\ so required probability \\ \begin{aligned} = 1 - \frac{24}{120} \\ = \frac{4}{5} \end{aligned} \end{aligned}$

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