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How many triangles can be created by connecting the vertices of a regular polygon with n (> 5) sides, ensuring that no triangle shares a side with the polygon?
- n / n-3C3
- nC3 - n - n(n-4)
- n-4C2 + n-3C3
- n+2C3
Correct answer: nC3 - n - n(n-4)
Solution
The number of triangles that can be created by connecting the vertices of a regular polygon with n sides is given by nC3 - n - n(n-4), which subtracts the triangles that share a side with the polygon.
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