Question

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

Answer 1

We get a line by joining two points. If $p$ are the number of lines from $21$ points, then
$p=C(21,2)=\frac{21!}{2!(21-2)!}$

$=\frac{21\times 20(19!)}{2\times 1(19!)}$
$=21\times 10=210$ lines