JEE Main · 2025 · 08 Apr 2025 · Shift 2 · Permutations and Combinations

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There are 12 points in a plane, no three of which are in the same straight line, except 5 points which are collinear. Then the total number of triangles that can be formed with the vertices at any three of these 12 points is

(A)230
(B)220
(C)200
(D)210✓ Correct

Answer: (D)

Solution

A triangle needs three non-collinear points. From the

12

points there are

(3 12) = 220

ways to choose three, but the

(3 5) = 10

choices lying entirely among the

5

collinear points form no triangle. Removing them leaves

220 - 10 = 210

triangles.

JEE Main · 2025 · 08 Apr 2025 · Shift 2 · Single correct option

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