Question

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

• A. $301$
• B. $210$
• C. $111$
• D. $220$

Answer 1

Answer: (B)

$210$

A chord is obtained by joining any two points on a circle. Therefore, total number of chords drawn through 21 points is same as the number of ways of selecting 2 points out of 21 points. This can be done in ${21}_{C_2}$ ways.

Hence, total number of chords = ${}^{21}{C}_2=\frac{21!}{19!2!}=21\times 10=210$