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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Permutation and Combination

NDA 2021 · Mathematics · Permutation and Combination

Consider a regular polygon with 10 sides. What is the number of...

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?

Options

  1. A25
  2. B50
  3. C75
  4. D100

Correct answer

B. 50

Step-by-step solution

We know that Triangle with no common side = total triangle (nC3)\left({ }^n C_3\right) - one side common triangles [n[n. (n−4)]−(n-4)]- Two side common triangles (n)(n). =n(n−4)(n−5)6=10(10−4)(10−5)6=\frac{n(n-4)(n-5)}{6}=\frac{10(10-4)(10-5)}{6}=50
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