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JEE MATHEMATICS MCQ: COMBINATIONS

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The straight lines I1,I2,I3I_1, I_2, I_3 are parallel and lie in the same plane. A total number of mm points on I1;nI_1 ; n points on I2;kI_2 ; k points on I3I_3, the maximum number of triangles formed with vertices at these points is
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Correct option: B
m+n+kC3−mC3−nC3−kC3{ }^{m+n+k} C_3-{ }^m C_3-{ }^n C_3-{ }^k C_3
Option B (m+n+kC3−mC3−nC3−kC3{ }^{m+n+k} C_3-{ }^m C_3-{ }^n C_3-{ }^k C_3) is correct because it subtracts the number of invalid triangles (formed by collinear points) from the total possible combinations of points.

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