There are 20 points in a plane, how many triangles can be formed by these points if 5 are collinear?

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{"type":"doc","content":[{"content":[{"marks":[{"type":"bold"}],"text":"Step 1 (Total unrestricted triangles):","type":"text"},{"text":" We want to form triangles by choosing 3 points out of 20. Without any collinear restrictions, the total ways is:","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"\text{Total Triangles} = \binom{20}{3} = \frac{20 \times 19 \times 18}{3 \times 2 \times 1} = 1140"},"type":"math_block"},{"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 2 (Subtract collinear selections):"},{"text":" We are given that 5 points are collinear. Choosing any 3 points from these 5 collinear points only forms a single straight line segment, not a triangle.","type":"text"},{"type":"hard_break"},{"type":"text","text":"The number of invalid choices is:"}],"type":"paragraph"},{"attrs":{"latex":"\text{Invalid Triangles} = \binom{5}{3} = 10"},"type":"math_block"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 3 (Subtract):","type":"text"},{"text":" Valid triangles = Total - Invalid:","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"\text{Valid Triangles} = 1140 - 10 = 1130"},"type":"math_block"},{"content":[{"text":"Step 4 (Conclusion):","type":"text","marks":[{"type":"bold"}]},{"text":" Exactly ","type":"text"},{"marks":[{"type":"code"}],"text":"1130","type":"text"},{"text":" triangles can be formed.","type":"text"}],"type":"paragraph"}]}

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