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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 20C_{2} ways.

∴ The total number of chords = 20C_{2 }

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

= `(20!)/(2! 8!)`

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

= 10 × 19

= 190

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