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Question

Consider the five points comprising of the vertices of a square and the intersection point of its diagonals. How many triangles can be formed using these points?


Solution

To form a triangle, $$3$$ points out of $$5$$ can be chosen in $$^{5}C_{3} = 10$$ ways.
But of these, the three points lying on the $$2$$ diagonals will be collinear.
So $$10 - 2 = 8$$ triangles can be formed.

Maths

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