Pentagons inside decagons

Probability Level 3

Using the vertices of a regular decagon how many pentagons can be made?


The answer is 252.

Ashish Menon by Ashish Menon , 20, India

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1 solution

Ashish Menon
May 15, 2016

We have to choose 5 points from 10 vertices of a decagon which can be found by 0 10 C 5 = 10 ! 5 ! × 5 ! = 5 ! × 30240 120 × 120 = 252 {\phantom{0}}^{10}C_{5}\\ = \dfrac{10!}{5! × 5!}\\ = \dfrac{5! × 30240}{120 × 120}\\ = \boxed{252}

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I think this should not be correct answer. If we choose 5 continuous points on decagon,we won't come up with a pentagon.

Devsmit Ranparia - 5 years, 1 month ago

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Why not? Even if we choose 5 continuous points after joining the last side a pentagon would be formed.

Ashish Menon - 5 years, 1 month ago

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I think you are right. I got my point. Thanks for discussion.

Devsmit Ranparia - 5 years, 1 month ago

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@Devsmit Ranparia – Feel free to discuss on anything :)

Ashish Menon - 5 years, 1 month ago

Answer should be 210. 10'C'4. Choose any 4 coordinates & close it by joining it with first coordinate.

Devsmit Ranparia - 5 years, 1 month ago

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No, then you will get a quadrilateral.

Ashish Menon - 5 years, 1 month ago

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