Polygon problem

Probability Level pending

Find the number of quadrilaterals that can be formed by selecting the corners of a 12 sided regular polygon such that NO side of polygon coincides with any side of the quadrilateral.


The answer is 105.

Nikitesh Soneji by Nikitesh Soneji , 31, India

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2 solutions

Harshi Singh
Aug 7, 2015

e a s y \formula easy \formula

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Dieuler Oliveira
Aug 20, 2014

g ( 12 , 4 ) = 12 − 4 4 ( 8 4 ) = 105 . g(12,4)=\frac{12-4}{4}{{8}\choose{4}}=\boxed{105}.

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hey, can u explain the formula used here ?

Siddharth Pandey - 6 years, 9 months ago

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Sure! This is called the 2 n d 2^{nd} Kaplansky's Lemma. You can find more about it here: Lemmas of Kaplansky

Dieuler Oliveira - 6 years, 9 months ago

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