As we know that 3 points are required to draw a triangle and the collinear points will lie on the same line.
The number of triangles formed = (total no. of triangles formed by all 12 points) – (no. of triangles formed by collinear points)
= 12C3 – 5C3
On using the formula,
nCr = n!/r!(n – r)!
= (2 × 11 × 10) – (5 × 2)
= 220 – 10
= 210
Hence, the total no. of triangles formed are 210.
