Four non-parallel lines in a plan intersect at most at

Question

Accepted Answer

{"content":[{"content":[{"marks":[{"type":"bold"}],"text":"Step 1 (Maximum Intersections Property):","type":"text"},{"text":" The maximum number of intersection points for ","type":"text"},{"attrs":{"latex":"n"},"type":"math_inline"},{"text":" non-parallel lines occurs when every pair of lines intersects at a unique point.","type":"text"}],"type":"paragraph"},{"content":[{"text":"Step 2 (Apply Combination):","type":"text","marks":[{"type":"bold"}]},{"type":"text","text":" The number of ways to choose a pair of lines out of "},{"attrs":{"latex":"n"},"type":"math_inline"},{"text":" is:","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"\text{Intersections} = \binom{n}{2} = \frac{n(n-1)}{2}"},"type":"math_block"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 3 (Substitute n = 4):","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"\text{Intersections} = \binom{4}{2} = \frac{4 \times 3}{2} = 6"},"type":"math_block"},{"type":"paragraph","content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 4 (Conclusion):"},{"text":" Four non-parallel lines intersect at most at ","type":"text"},{"marks":[{"type":"code"}],"text":"6","type":"text"},{"text":" points.","type":"text"}]}],"type":"doc"}

Guide / Hint

Solution