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Question
How many chords can be drawn through 20 points on a circle?
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 = 20C2
= `(20!)/(2!(20 - 2)!)`
= `(20!)/(2! 8!)`
= `(20 xx 19 xx 18!)/(2 xx 1 xx 18!)`
= 10 × 19
= 190
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