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Question

We are given 6 non collinear line segments with length 2,3,4,5,6,7 unit. Number of triangles that can be made by these line segments are

A

6C37
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B
6C36
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C
14
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D
13
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Solution

The correct options are
A
6C37
D 13
As we know three line segments are required to form a triangle.
Number of ways to select 3 line segments out of 6 = 6C3.
But (2,3,7),(2,3,6),(2,3,5),(2,4,6),(2,4,7),(2,5,7),(3,4,7) do not form triangle.
So required number of triangles are : 6C37

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