JEE Main 202523 JanuaryEvening Shift
- Exam
- JEE Main
- Year
- 2025
- Date
- 23 January
- Shift
- Evening Shift
- Subject
- Mathematics
- Chapter
- Probability
JEE Main 2025 · 23 January · Evening Shift · Mathematics · Probability
A board has 16 squares as shown in the figure: Out of these 16...
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 :
Options
- A7/10
- B4/5
- C23/30
- D3/5
Correct answer
B. 4/5
Step-by-step 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}