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555-605 Level|   Combinations|   Geometry|      
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Bunuel
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Eight points lie on the circumference of a circle What is the positive 06 Jan 2021, 08:57
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79% (01:40) correct 21% (01:57) wrong based on 131 sessions

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Eight 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 formed by connecting these points?

A. 8

B. 14

C. 56

D. 70

E. 1,344
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B
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Eight points lie on the circumference of a circle What is the positive 06 Jan 2021, 14:09
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The problem is a Combinations one:


For the Triangles there are 8!/(3!*5!) ways of joining the 8 dots on the circle.
= 56

For the quadrilateral, there are 8!(4!4!) ways of joining the 8 dots on the circle
= 70

The positive difference is therefore (B) 14
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Eight points lie on the circumference of a circle What is the positive 06 Jan 2021, 14:21
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Given, 8 points were not collinear.

Difference = No. of quadrilaterals - No. of triangles = 8C4 - 8C3 = 70- 56 = 14

So, I think B. :)
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Eight points lie on the circumference of a circle What is the positive 07 Jan 2021, 01:14
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3 points to form triangles selected from 8 points: \(^8{C_3} = 56\)

4 points to form quadrilaterals selected from 8 points: \(^8{C_4} = 70\)

=> 70 - 56 = 14

Answer B
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Eight points lie on the circumference of a circle What is the positive 17 Jan 2021, 12:25
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Bunuel
Eight 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 formed by connecting these points?

A. 8

B. 14

C. 56

D. 70

E. 1,344
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Solution:

Since the 8 points are on the circumference of a circle, no three of them are collinear. So any set of three points will form a triangle and any set of four points will form a quadrilateral. Since the number of triangles that can be formed is 8C3 = (8 x 7 x 6) / (3 x 2) = 56 and the number of quadrilaterals that can be formed is 8C4 = (8 x 7 x 6 x 5) / (4 x 3 x 2 x 1) = 2 x 7 x 5 = 70, therefore, the positive difference between the number of triangles and quadrilaterals that can be formed is 70 - 56 = 14.

Answer: B
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Eight points lie on the circumference of a circle What is the positive 15 Feb 2021, 22:09
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# of quadrilaterals that can be formed with 8 points is 8C4 = 70 <--- quadrilaterals have 4 sides
# of triangles that can be formed with 8 points is 8C3 = 56

70 - 56 = 14

B.
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Eight points lie on the circumference of a circle What is the positive 06 Dec 2024, 07:26
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