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.
  ${}^6{C}_3-7$
• B. ${}^6{C}_3-6$
• C. $14$
• D. $13$

Answer 1

Answer: (A), (D)

The correct options are
A
${}^6{C}_3-7$
D $13$

As we know three line segments are required to form a triangle.
Number of ways to select $3$ line segments out of $6$ $={}^6{C}_3$.
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 $:{}^6{C}_3-7$