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Sum

If 20 points are marked on a circle, how many chords can be drawn?

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#### Solution

To draw a chord we need to join two points on the circle.

There are 20 points on the circle.

∴ We can draw ^{20}C_{2 }chords of the circle.

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

= `(20!)/(18!2!)`

= `(20 xx 19xx18!)/(2xx1xx18!)`

= 190

190 chords can be drawn.

Concept: Properties of Combinations

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