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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.
\[ = \frac{12}{3} \times \frac{11}{2} \times \frac{10}{1} - \frac{5}{3} \times \frac{4}{2} \times \frac{3}{1} \]
\[ = 220 - 10 \]
\[ = 210\]
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