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Previous Year Question (PYQs)
2
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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