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Previous Year Question (PYQs)



If six out of ten points in a plane are collinear, then the number of triangles formed by joining these points will be ... 100.





Solution

Total triangles from 10 points $= \binom{10}{3} = 120.$ Triangles not possible from 6 collinear points $= \binom{6}{3} = 20.$ Hence, number of triangles formed $= 120 - 20 = 100.$ Since result equals 100, the number is $\ge$ 100.


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