<p>There are 10 points on a plane of which no three points are collinear. If lines are formed joining these points, find the maximum points of intersection of these lines.</p>
Step-by-Step Solution
Key Concept: Each pair of lines intersects at exactly one point, and each pair of lines is uniquely determined by choosing 4 points (2 points for each line). Therefore, the maximum intersection points equals the number of ways to choose 4 points from 10, which is ¹⁰C₄.
<p><strong>Step 1:</strong> Find the total number of lines formed by joining 10 points where no three are collinear. This is ¹⁰C₂ = 45 lines.</p><p><strong>Step 2:</strong> Each pair of distinct lines intersects at exactly one point (since no three points are collinear, no two lines are parallel or coincident).</p><p><strong>Step 3:</strong> The number of ways to choose 2 lines from 45 lines is ⁴⁵C₂.</p><p><strong>Step 4:</strong> Calculate: ⁴⁵C₂ = (45 × 44)/2 = 990 intersection points.</p><p>∴ Answer: ⁴⁵C₂ or 990</p>
Correct Answer: ⁴⁵C₂