2 diagonals of a regular heptagon (a 7-sided polygon) are chosen. What is the probability that they intersect inside the heptagon?

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2 diagonals of a regular heptagon (a 7-sided polygon) are chosen. What is the probability that they intersect inside the heptagon?

I've been stuck on this problem for uite a while. I know that there arer 30 diagonals, but that is as far as I got.

Thanks!

Guest Oct 28, 2018

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1⁺⁰ Answers

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First of all, there are 14 diagonals, not 30 diagonals. This can be found by \(\dfrac{n(n-3)}{2}=\dfrac{7*4}{2}=14\) diagonals. Is the answer 28+42/182(5/13), because we can choose the first diagonal is 14 ways, the second is 13.

tertre Oct 28, 2018

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