Combinatorics II problem by Pr. Fares Salem

Probability Level 1

How many diagonals does a 2007-gon have?


The answer is 2011014.

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Fares Salem by Fares Salem , 22, Egypt

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3 solutions

Samanvay Vajpayee
Nov 14, 2014

n(n-3) /2 direct formula substitution

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Thank You :)

Fares Salem - 6 years, 7 months ago

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you are welcome :)

Samanvay Vajpayee - 5 years, 6 months ago
Mohit Khanwale
Feb 7, 2015

2007 C 2 - 2007 = 2011014

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Fares Salem
Oct 17, 2014

From each vertex emanate 2007−3 = 2004 diagonals. But each diagonal connects two vertices,

so the total is 2007 · 2004/2 = 2011014

0 Helpful 0 Interesting 0 Brilliant 0 Confused

The formula for calculating the no. of diagonals of a n -sided polygon is given by;- n(n-3)/2 Therefore, no.of diagonals = 2007(2004)/2 = 2011014

Panshul Rastogi - 6 years, 7 months ago

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