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In a plane 8 points are colliner out of 12 points, then the number of triangles we get with those 12 points is

Correct Answer: 164

Explanation:

For a triangle, we need 3 non-collinear points. So with 12 points (when all the 12 are such that any three non-collinear is 12 C 3 . But among them 8 points are collinear.


 


If all these 8 points are different we get  8 C 3  triangles as they are collinear.


 


In  12 C 3  triangles, we do not get  8 C 3  triangles


 


Therefore, The number of triangles we get = 12 C 3 - 8 C 3  = 164


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