Question

Given five line segments of length $2,3,4,5,6$ units. Then the number of triangles that can be formed by joining these lines is

• A. ${}^5{C}_3-3$
• B. ${}^5{C}_3-1$
• C. ${}^5{C}_3$
• D. ${}^5{C}_3-2$

Answer 1

The correct option is A ${}^5{C}_3-3$

We know that in any triangle the sum of two sides is always greater than the third side.

$\therefore$ The triangle will not be formed is we select segments of lengths $(2,3,5),(2,3,6)$ or $(2,4,6)$.

Hence number of triangles formed ${}^5{C}_3-3$.