Engineering
Mathematics
Introduction to Determinants
Question
The straight lines I1, I2 and I3 are parallel and lie in the same plane. A total of m points are taken on the line I1 n points on I2, and k points on I3. How many triangles are there whose vertices are at these points?
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Solution
There are total n + m + k points.
And a triangle can't be formed if all the three points are on the same line.
Total number of ways to select three points = n+m+kC3
And, number of ways to select three points on the same line = mC3 + nC3 + kC3
Hence, required number of triangles formed
= n+m+kC3 – (nC3 + mC3 + kC3)
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