Question

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

Answer 1

There are 21 points on the circumference of a circle. Since one and only one chord can be drawn by joining 2 distinct points, the required number of chords is given by:

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