Tamil Nadu Board of Secondary EducationHSC Science Class 11

How many chords can be drawn through 20 points on a circle? - Mathematics

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Sum

How many chords can be drawn through 20 points on a circle?

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Solution

Number given points on the circle = 20

A chord is obtained by joining any two points on the circle.

‘Number of chords drawn through 20 points is same as the number of ways of selecting 2 points out of 20 points.

This can be done 20C2 ways.

∴ The total number of chords = 20C

= `(20!)/(2!(20 - 2)!)`

= `(20!)/(2!  8!)`

= `(20 xx 19 xx 18!)/(2 xx 1 xx 18!)`

= 10 × 19

= 190

Concept: Combinations
  Is there an error in this question or solution?
Chapter 4: Combinatorics and Mathematical Induction - Exercise 4.3 [Page 186]

APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 11th Mathematics Volume 1 and 2 Answers Guide
Chapter 4 Combinatorics and Mathematical Induction
Exercise 4.3 | Q 9. (iii) | Page 186

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