Selection Of Consecutive Objects

Question

From 20 points placed on a straight line, the number of line segments that can be formed by joining any two of these points equals which value?

RankGuru · Accepted Answer

A line segment is determined by an unordered pair of distinct points, so the count is a simple combination, a basic JEE Advanced application. With 20 points, the number of ways to choose 2 of them is C(20, 2) = (20 × 19)/2 = 190. Each chosen pair gives exactly one segment, and order does not matter since the segment from P to Q is the same as from Q to P. Option 400 = 20^2 counts ordered pairs including a point with itself. Option 20 counts only the points. Option 380 = 20 × 19 counts ordered pairs of distinct points, double counting each segment. Hence there are 190 segments. Plausibility check: dividing the ordered count 20 × 19 = 380 by 2 to remove direction gives 190, matching the combination C(20,2) and confirming that each unordered pair yields one segment.

Selection Of Consecutive Objects

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