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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Eight points lie on the circumfrence of a circle
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ldoolitt
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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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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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