Question

Given $5$ line segments of lengths $2, 3, 4, 5, 6$ units. Then, the no. of triangles that can be formed by joining these segments is

• A. $^5C_3 - 3$
• B. $^5C_3$
• C. $^5C_3 - 1$
• D. $^5C_3 - 2$

Answer 1

Answer: (A)

$^5C_3 - 3$

Answer 2

To form a triangle, 3 line segments are needed.
We can choose 3 line segment from 5 line segments in $^5C_3$ ways.
We know that in a triangle, sum of two sides is always greater than third side.
So, line segments of length (2, 3, 5), (2, 3, 6) and (2, 4, 6) do not form any triangle.
$\therefore$ Total number of triangles formed = $^5C_3 - 3$