How many triangles can be obtained by joining 12 points,
Question:

How many triangles can be obtained by joining 12 points, five of which are collinear?

Solution:

Out of 12 points, 5 points are collinear and 3 points are required to form a triangle.

Required ways $={ }^{12} C_{3}-{ }^{5} C_{3}$

$=\frac{12}{3} \times \frac{11}{2} \times \frac{10}{1}-\frac{5}{3} \times \frac{4}{2} \times \frac{3}{1}$

$=220-10$

 

$=210$

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