How many chords can be drawn through $21$ points on a circle?
How many chords can be drawn through $21$ points on a circle?
For drawing one chord 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 $=\,^{21} C_{2}=\frac{21 !}{2 !(21-2) !}=\frac{21 !}{2 ! 19 !}=\frac{21 \times 20}{2}=210$
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