We know that 3 points are required to draw a triangle and the collinear points will lie on the same line.
Number of triangles formed = (total no. of triangles formed by all 12 points) – (no. of triangles formed by collinear points)
= 12C3 – 5C3
By using the formula,
nCr = \(\dfrac{ n!}{r!(n – r)!}\)
= (2×11×10) – (5×2)
= 220 – 10
= 210
The total no. of triangles formed are 210.
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