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Question

The number of diagonals and triangles formed in an octagon are

A
20,56
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B
32,58
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C
30,58
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D
32,56
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Solution

The correct option is D 20,56
Let A1,A2,........,A8 be the vertices of the octagon.
One triangle is formed by selecting a group of 3 points from 8 given vertices.
No. of triangles = No. of groups of 3 each from 8 points = 8C3=8.7.66=56
(b) No. of lines that can be formed by using the given vertices of a polygon = No. of groups of 2 points each selected from the n points
=8C2=28
Out of these 8 are the sides of the polygon and remaining(288) are the diagonals = 20
Hence, option 'A' is correct.

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