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  • How many triangles can you form on a plane with 15 non-collinear points?  Option: 1 345O

How many triangles can you form on a plane with 15 non-collinear points?

 

Option: 1

345


Option: 2

455


Option: 3

545


Option: 4

625


Answers (1)

best_answer

Given that,

There are 15 non-collinear points on a plane.

To form a triangle we need 3 non-collinear points.

Thus, we have 15 points, so we have to choose 3 out of 15 points.

This is given by,

\mathrm{ { }^{15} C_3=\frac{15 !}{3 ! 12 !} }

\mathrm{{ }^{15} C_3=\frac{15 \times 14 \times 13}{3 \times 2}}

\mathrm{{ }^{15} C_3=5 \times 7 \times 13}

\mathrm{{ }^{15} C_3=455}

Therefore, the number of triangles formed is 455.

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