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Eight points lie on the circumfrence of a circle

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by abhi332 » Wed Feb 24, 2010 12:00 pm
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

[spoiler]OA: B[/spoiler]
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by ldoolitt » Wed Feb 24, 2010 1:02 pm
abhi332 wrote: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

[spoiler]OA: B[/spoiler]

Weeeel. Its a combinatorics problem.

Any 3 points that lie on a circle will form a triangle. Any 4 points that lie on a circle will form a quadrilateral. So the question is reduced to how many ways can you choose 4 points from 8 and 3 points from 8.

8C4 - 8C3 = 70 - 56 = 14

Choose (b)
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Re: Eight points lie on the circumfrence of a circle

by Scott@TargetTestPrep » Fri Jan 15, 2021 10:33 am
abhi332 wrote: ↑
Wed Feb 24, 2010 12:00 pm
 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

[spoiler]OA: B[/spoiler]
Solution:

Since the 8 points are on the circumference of a circle, no three of them are collinear. Therefore, 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 is 70 - 56 = 14.

Answer: B

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Re: Eight points lie on the circumfrence of a circle

by swerve » Fri Jan 15, 2021 5:59 pm
abhi332 wrote: ↑
Wed Feb 24, 2010 12:00 pm
 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

[spoiler]OA: B[/spoiler]
Given, 8 points were not collinear.

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

Therefore, B
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