Question

How many different chords are determined by 8 distinct points lying on a circle?

• A. 40
• B. 18
• C. 32
• D. 28

Answer 1

The correct option is D 28

Selection of $1^{st}$ point can be done in 8 ways (8 points) and the $2^{nd}$ point can be done in 7 ways (remaining points).
Removing the duplicates (due to double counting of chords), we have number of different chords = $\frac{1}{2}\times 7\times 8=28$.