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 $={ }^{12} C_{3}-{ }^{5} C_{3}$
$=\frac{12}{3} \times \frac{11}{2} \times \frac{10}{1}-\frac{5}{3} \times \frac{4}{2} \times \frac{3}{1}$
$=220-10$
$=210$