Question:
The number of diagonals in a regular polygon of $100$ sides is
The number of diagonals in a regular polygon of $100$ sides is
Updated On: Feb 2, 2024
- 4950
- 4850
- 4750
- 4650
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The Correct Option is B
Solution and Explanation
The number of diagonals in a regular polygon of $n$ sides is given by the following formula ${ }^{n} C_{2}-n$
$\therefore$ The number of diagonals in a regular polygon of 100 sides
$={ }^{100} C_{2}-100=\frac{100 \cdot 99}{2}-100$
$=\frac{9900-200}{2} =\frac{9700}{2}=4850$
$\therefore$ The number of diagonals in a regular polygon of 100 sides
$={ }^{100} C_{2}-100=\frac{100 \cdot 99}{2}-100$
$=\frac{9900-200}{2} =\frac{9700}{2}=4850$
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Concepts Used:
Combinations
The method of forming subsets by selecting data from a larger set in a way that the selection order does not matter is called the combination.
- It means 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.
- For example, Imagine you go to a restaurant and order some soup.
- Five toppings can complement the soup, namely:
- croutons,
- orange zest,
- grated cheese,
- chopped herbs,
- fried noodles.
But you are only allowed to pick three.
- There can be several ways in which you can enhance your soup with savory.
- The selection of three toppings (subset) from the five toppings (larger set) is called a combination.
Use of Combinations:
It is used for a group of data (where the order of data doesn’t matter).