A board has 16 squares as show in the figure: Out of these 16 squares, two squares are chosen at random. The probability that they have no side in common is: [2025]

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Solution

Q.
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: [2025]

1 $\frac{4}{5}$

2 $\frac{3}{5}$

3 $\frac{7}{10}$

4 $\frac{23}{30}$

Ans.
(1)

Total ways for selecting any two squares $= {}^{16}C_{2} = 120$

Total ways for selecting common side squares $= \underset{Horizontal side}{\underset{⏟}{3 \times 4}} + \underset{Vertical side}{\underset{⏟}{3 \times 4}} = 24$

So, required probability $= 1 - \frac{24}{120} = \frac{96}{120} = \frac{4}{5}$ .

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