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Question -

How many triangles can be obtained by joining 12 points, five of which are collinear?



Answer -

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 = n!/r!(n – r)!

= (2×11×10) – (5×2)

= 220 – 10

= 210

∴ The total no. oftriangles formed are 210.

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