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The number of pentagons that can be inscribed in an octagon

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Senior Manager
Joined: 20 May 2014
Posts: 282
Followers: 14

Kudos [?]: 49 [0], given: 220

The number of pentagons that can be inscribed in an octagon [#permalink]  22 Oct 2017, 06:15
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Question Stats:

100% (01:35) correct 0% (00:00) wrong based on 3 sessions
 Quantity A Quantity B The number of pentagons that can be inscribed in an octagon The number of triangles that can be inscribed in an octagon

(A) The quantity in Column A is greater
(B) The quantity in Column B is greater
(C) The two quantities are equal
(D) The relationship cannot be determined from the information given

Kudos for correct solution.
[Reveal] Spoiler: OA
Director
Joined: 03 Sep 2017
Posts: 521
Followers: 1

Kudos [?]: 327 [0], given: 66

Re: The number of pentagons that can be inscribed in an octagon [#permalink]  22 Oct 2017, 09:05
Since a pentagon has 5 vertices, in order to compute how many pentagons in an octagon, which, instead, has eight vertices, we can compute the number of ways in which we can take 5 vertices out of 8. Computing the number of pentagons that can be inscribed in an octagon amounts to compute in how many ways we can choose 5 points out of 8, i.e. $$8C5 = \frac{8!}{5!3!}$$. The same holds for the number of triangles, i.e. they can be computed as $$8C3 = \frac{8!}{3!5!}$$. The two quantities are then equal and answer is C!.
Re: The number of pentagons that can be inscribed in an octagon   [#permalink] 22 Oct 2017, 09:05
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