Question:

<p><strong>Step 1: Find total ways to choose 2 squares from 64</strong></p><p>A standard chessboard has 8 × 8 = 64 squares.</p><p>Total ways to choose 2 squares = $\binom{64}{2} = \frac{64 \times 63}{2} = \frac{4032}{2} = 2016$</p><p><strong>Step 2: Count pairs of squares with a common side</strong></p><p>Two squares have a common side if they are adjacent horizontally or vertically (not diagonally).</p><p>For horizontal adjacencies: In each row of 8 squares, there are 7 pairs of adjacent squares. With 8 rows, we have 8 × 7 = 56 horizontal pairs.</p><p>For vertical adjacencies: In each column of 8 squares, there are 7 pairs of adjacent squares. With 8 columns, we have 8 × 7 = 56 vertical pairs.</p><p>Total pairs with common side = 56 + 56 = 112</p><p><strong>Step 3: Calculate the probability</strong></p><p>Probability = $\frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{112}{2016}$</p><p>Simplify the fraction:</p><p>$\frac{112}{2016} = \frac{112}{2016} = \frac{7}{126} = \frac{1}{18}$</p><p>To verify: $112 = 2^4 \times 7$ and $2016 = 2^5 \times 3^2 \times 7$</p><p>$\frac{112}{2016} = \frac{2^4 \times 7}{2^5 \times 3^2 \times 7} = \frac{1}{2 \times 9} = \frac{1}{18}$</p><p><strong>∴ Answer: B</strong></p>