JEE MAIN - Mathematics (2025 - 23rd January Evening Shift - No. 5)
A board has 16 squares as shown in the figure :
_23rd_January_Evening_Shift_en_5_1.png)
Out of these 16 squares, two squares are chosen at random. The probability that they have no side in common is :
$\frac{3}{5}$
$\frac{4}{5}$
$\frac{23}{30}$
$\frac{7}{10}$
Explanation
Total ways for selecting any two squares $={ }^{16} \mathrm{C}_2=120$
Total ways for selecting common side squares
_23rd_January_Evening_Shift_en_5_2.png)
$$\begin{aligned} &=24\\ &\text { so required probability }\\ &\begin{aligned} & =1-\frac{24}{120} \\ & =\frac{4}{5} \end{aligned} \end{aligned}$$
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