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Solution


Q.

There are 12 points in a plane, no three of which are in the same straight line, except 5 points which are collinear. Then the total number of triangles that can be formed with the vertices at any three of these 12 points is          [2025]
1 200  
2 210  
3 230  
4 220  

Ans.

(2)

The number of ways to choose 3 points from 12 = C312

                                                                             = 12×11×103×2×1 = 220

Number of ways to choose 3 points from 5 collinear points = C35 = 10

Since these 5 points are collinear, so they can not form any triangles.

∴   Number of triangles that can be formed = 220 –10 = 210