Among all convex polygons with n sides, the maximum number of points of intersection of the diagonals inside the polygon is 330. The value of n is
Explanation:
By selecting 4 vertices we can get exactly one pair of diagonals which will intersect each other.
∴ The maximum number of points of intersection of the diagonals inside the polygon is same as selecting 4 vertices i.e., nC4.
⇒ nC4 = 330
⇒ n(n-1)(n-2)(n-3)4×3×2×1 = 330
⇒ n(n – 1) (n – 2)(n – 3) = 11 × 10 × 3 × 4 × 3 × 2
⇒ n(n – 1) (n – 2)(n – 3) = 11 × 10 × 9 × 8
⇒ n = 11
Hence, 11.
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.