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
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
Updated On: May 11, 2024
- $^5C_3 - 3$
- $^5C_3 $
- $^5C_3 - 1$
- $^5C_3 - 2$
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The Correct Option is A
Solution and Explanation
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 = $^5C_3 - 3$
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 = $^5C_3 - 3$
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Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.