Find the maximum number of triangles that may be created by selecting the vertices from a group of 15 points, ten of which are on the same straight line.
335
225
445
525
Three points are required to make a triangle, hence 15 points result in triangles.
The total number of triangles formed from 15 points =
Thus,
However, in a statement that was made very clear, 10 points were in the same line and formed a triangle in ways.
Thus,
It is known that the 10 points are on the same line.
So, the 10 points out of 15 are given by,
Therefore, the number of triangles formed is 335.
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