Question:
How many chords can be drawn through 21 points on a circle?
How many chords can be drawn through 21 points on a circle?
Updated On: Apr 4, 2024
Hide Solution
Verified By Collegedunia
Solution and Explanation
For drawing one chord on a circle, only 2 points are required.
To know the number of chords that can be drawn through the given 21 points on a circle, the number of combinations have to be counted.
Therefore, there will be as many chords as there are combinations of 21 points taken 2 at a time.
Thus, required number of chords
\(=\space^{21}C_2=\frac{2!}{2!\left(21-2\right)!}\)
\(=\frac{21!}{2!19!}\)
\(=\frac{21\times20}{2}\)
\(=210\)
Was this answer helpful?
1
0
Top Questions on permutations and combinations
- A mother was asked how many gifts she had in the bag. She replied that there were dolls but six, cars but six, and all books but six. How many gifts had she in all?
- Karnataka PGCET - 2025
- Quantitative Aptitude
- permutations and combinations
- A person needs to find the fastest two horses from 16 horses. Only a race of 4 horses can be conducted at a time. What is the minimum number of races to be conducted to determine the fastest two? (Assume that horses will not get tired at all and time cannot be measured)
- Karnataka PGCET - 2025
- Quantitative Aptitude
- permutations and combinations
- In a school, 120 boys have registered for a singles carrom tournament. Each match eliminates one player. How many matches are to be organized to determine the champion?
- Karnataka PGCET - 2025
- Quantitative Aptitude
- permutations and combinations
- In how many ways can a chairperson, a secretary, and a treasurer be chosen from a group of 10 people, if each person can hold only one position?
- AP PGECET - 2025
- Mathematics
- permutations and combinations
How many possible words can be created from the letters R, A, N, D (with repetition)?
- NATA - 2025
- Quantitative Aptitude
- permutations and combinations
View More Questions
Questions Asked in CBSE Class XI exam
- We have carefully distinguished between average speed and magnitude of average velocity. No such distinction is necessary when we consider instantaneous speed and magnitude of velocity. The instantaneous speed is always equal to the magnitude of instantaneous velocity. Why?
- CBSE Class XI
- Motion in a straight line
- If U = {a, b, c, d, e, f, g, h}, find the complements of the following sets:
(i) A = {a, b, c}
(ii) B = {d, e, f, g}
(iii) C = {a, c, e, g}
(iv) D = {f, g, h, a}- CBSE Class XI
- Complement of a Set
- What are the oxidation numbers of the underlined elements in each of the following and how do you rationalise your results?
(a) KI3 (b) H2S4O6 (c) Fe3O4 (d) CH3CH2OH (e) CH3COOH- CBSE Class XI
- Oxidation Number
- Using s, p, d notations, describe the orbital with the following quantum numbers.
- n=1, l=0
- n = 3, l=1
- n = 4, l =2
- n=4, l=3
- CBSE Class XI
- Developments Leading to the Bohr’s Model of Atom
- Write the following as intervals:
(i) {\(x: x ∈ R, -4 < x ≤ 6\)}
(ii) {\(x: x ∈ R, -12 < x < -10\)}
(iii) {\(x: x ∈ R, 0 ≤ x < 7\)}
(iv) {\(x: x ∈ R, 3 ≤ x ≤ 4\)}- CBSE Class XI
- Sets and their Representations
View More Questions
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.