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Permutations & Combinations
Combinations with collinear points
nta_pyq_2025_apr
Grade 12

Question:

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
$230$
$220$
$200$
$210$

Step-by-Step Solution

Key Concept: Count all triangles from$12$points and subtract degenerate triples from the$5$collinear points.
12$C_{3} - 5$$C_{3} = 210$$(4)$
Correct Answer: 4

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