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

Step-by-step solution

Number of points = 21 ⇒ n = 21 A chord connects circle at two points. ⇒ r = 2 ∴ Number of chords from 21 points on a circle = C r n ∴ C r n = C 2 21 = 21 ! 19 ! × 2 ! = 21 × 20 × 19 ! 19 ! × 2 × 1 = 210 ∴ 210 chords can be drawn through 21 points on a circle.