Question

How many chords can be drawn through 21 points on a circle?

Answer 1

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
$=\space^{21}C_2=\frac{2!}{2!\left(21-2\right)!}$

$=\frac{21!}{2!19!}$

$=\frac{21\times20}{2}$
$=210$