First slide

Combinations

Question

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

Moderate

A

$^{5} C_{3} - 3$
B

$^{5} C_{3} - 1$
C

$^{5} C_{3}$
D

$^{5} C_{3} - 2$

Solution

We know that in any triangle the sum of two sides is always greater than the third side.
$∴$ The triangle will not be formed if we select segments of lengths (2, 3, 5), (2, 3, 6) or (2, 4, 6).
Hence number of triangles formed $=^{5} C_{3} - 3$ .

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