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# Six points lie on the circumference of a circle. What is the

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Senior Manager
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Six points lie on the circumference of a circle. What is the [#permalink]  05 Oct 2009, 05:11
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Six points lie on the circumference of a circle. What is the positive difference between the number of triangles and the number of quadrilaterals that can be created by connecting these points?

A. 4
B. 5
C. 6
D. 15
E. 20
[Reveal] Spoiler: OA

Last edited by Bunuel on 16 Aug 2014, 06:34, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Senior Manager
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Re: Six points lie on the circumference of a circle. What is the [#permalink]  05 Oct 2009, 05:43
6c3-6c4=6.5.4/3.2.1-6.5.4.3/4.3.2.1=20-15=5
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Re: Six points lie on the circumference of a circle. What is the [#permalink]  16 Aug 2014, 06:06
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Six points lie on the circumference of a circle. What is the [#permalink]  25 Aug 2014, 21:19
Let's start with the triangle: You have 6 points to choose from but only 3 points you will connect and 3 points you will not connect.

Hence number of possibilities for triangle: 6! / 3! * 3! = 20

Same goes for the quadrilateral: 6 points to choose from, 4 points which you will connect and 2 points which you won't connect.

Number of possibilities for quadrilateral: 6! / 4! * 2! = 15

Difference = 5

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Re: Six points lie on the circumference of a circle. What is the [#permalink]  25 Aug 2014, 22:49
$$\frac{6!}{3!3!} - \frac{6!}{4!2!} = 20 - 15 = 5$$

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Re: Six points lie on the circumference of a circle. What is the [#permalink]  13 Oct 2014, 03:26
study wrote:
Six points lie on the circumference of a circle. What is the positive difference between the number of triangles and the number of quadrilaterals that can be created by connecting these points?

A. 4
B. 5
C. 6
D. 15
E. 20

Number of triangles can be formed out of 6 points= 6C3=20
Number of quadrilaterals can be formed out of 6 points= 6C4=15

20-15=5.

Re: Six points lie on the circumference of a circle. What is the   [#permalink] 13 Oct 2014, 03:26
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