Question

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

Answer 1

We know that to draw a chord of a circle, only $2$ points are required.

So,the number of chords that can be drawn through the given $21$ points on a circle is

${}^{21}{C}_2=\frac{21!}{2!(21-2)!}=\frac{21!}{2!19!}=\frac{21\times 20}{2}=210$