Question:
The number of diagonals of a polygon of $20$ sides is
The number of diagonals of a polygon of $20$ sides is
Updated On: Jun 23, 2024
- $ 210 $
- $ 190 $
- $ 180 $
- $ 170 $
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The Correct Option is D
Solution and Explanation
Number of diagonals in a polygon of n sides
$ {{=}^{n}}{{C}_{2}}-n $
Here, $ n=20 $
$ \therefore $ Required number of diagonals
$ {{=}^{20}}{{C}_{2}}-20 $
$ =\frac{20\times 19}{2\times 1}-20 $
$ =170 $
$ {{=}^{n}}{{C}_{2}}-n $
Here, $ n=20 $
$ \therefore $ Required number of diagonals
$ {{=}^{20}}{{C}_{2}}-20 $
$ =\frac{20\times 19}{2\times 1}-20 $
$ =170 $
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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.
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- 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.