Question

A circle has $n$ points on its circumference. What is the maximum number of points of intersection of chords inside the circle?

Answer 1

To form a pair of chords that intersect, we need 4 points.

Given that the circle has n points on its circumference.

$\therefore$ total no. of pair of chords that intersects $=n_{C_4}$

Since there is only one way to join the $4$ points with two chords and form an intersection.

Hence, the final answer is $n_{C_4}$.