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Question
How many chords can be drawn through 21 points on a circle?
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Solution
For drawing one chord on a circle, only 2 points are required.
To know the number of chords that can be drawn through the given 21 points on a circle, the number of combinations have to be counted.
Therefore, there will be as many chords as there are combinations of 21 points taken 2 at a time.
Thus, required number of chords =
= 21C2 = `(21!)/(2!(21 - 2)!) = (21!)/(2!19!)`
= `(21 xx 20)/(1 xx 2)`
= 210
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