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4. Use combinations to find the maximum number of points of intersection determined by the diagonals of a convex n-gon in its interior. Notice that the diagonals of a pentagon determine a maximum number of 5 points of intersection in its interior. Explain why the process is correct. E

4. Use combinations to find the maximum number of points of intersection determined by the diagonals of a convex n-gon in its interior. Notice that the diagonals of a pentagon determine a maximum number of 5 points of intersection in its interior. Explain why the process is correct. E

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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4. Use combinations to find the maximum number of points of intersection determined by the diagonals of a convex n-gon in its interior. Notice that the diagonals of a pentagon determine a maximum number of 5 points of intersection in its interior. Explain why the process is correct. E B.
Transcribed Image Text:4. Use combinations to find the maximum number of points of intersection determined by the diagonals of a convex n-gon in its interior. Notice that the diagonals of a pentagon determine a maximum number of 5 points of intersection in its interior. Explain why the process is correct. E B.
Expert Solution
Step 1

Let A be a set of n elements. To select r objects from a collection of n elements in the set A without repetition, use the combination formula

nCr=n!r!n-r!.

The value of the factorial can be calculated by the formula n!=nn-1n-2 ⋯ 21.

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