<p>Find the number of ways in which two small squares can be selected on the normal chessboard if they are not in same row or same column.</p>
Step-by-Step Solution
Key Concept: First count total ways to select 2 squares from 64, then subtract cases where both squares share the same row or column. Use complementary counting: Total - (same row) - (same column).
<p><strong>Step 1:</strong> Total ways to select 2 squares from a chessboard = C(64,2) = (64 × 63)/2 = 2016</p><p><strong>Step 2:</strong> Count pairs in the SAME ROW: There are 8 rows, each with 8 squares. Ways to select 2 from 8 squares in one row = C(8,2) = 28. Total for all 8 rows = 8 × 28 = 224</p><p><strong>Step 3:</strong> Count pairs in the SAME COLUMN: Similarly, there are 8 columns, each with 8 squares. Ways to select 2 from 8 squares in one column = C(8,2) = 28. Total for all 8 columns = 8 × 28 = 224</p><p><strong>Step 4:</strong> Apply complementary counting: Pairs NOT in same row AND NOT in same column = 2016 - 224 - 224 = <strong>1568</strong></p>
Correct Answer: 1568