How many chords can be drawn through 21 points on a circle?

Solution:

We will be using the concept of permutations and combinations to solve this.

No. of points (n) = 21
No. of points to be used to form a chord (r) = 2

To form a chord, 2 points out of 21 points should be selected and it can be done in ²¹C₂ ways.

Thus, the total number of ways = ²¹C₂
= 21! / [2!(21 - 2)!]
= 21! / [2!(19)!] (Using nCr formula)
= (21×20×19!) / (2×19!)
= (21×20) / 2
= 21×10
= 210

NCERT Solutions Class 11 Maths Chapter 7 Exercise 7.4 Question 3

How many chords can be drawn through 21 points on a circle?

Summary:

The number of chords that can be drawn through 21 points on a circle is 210