Q205 / 270 · NDA 2021 (Phase 2) · Mathematics

Consider a regular polygon with 10 sides. What is the number of triangles that can be formed by joining the vertices which have no common side with any of the sides of the polygon?

  • A
    25
  • Correct answer
    B
    50
  • C
    75
  • D
    100

Solution

We know that Triangle with no common side $=$ total triangle $\left({ }^n C_3\right)$ - one side common triangles $[n$. $(n-4)]-$ Two side common triangles $(n)$. $=\frac{n(n-4)(n-5)}{6}=\frac{10(10-4)(10-5)}{6}=50$

Hence, the correct answer is option: 'B'.

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