Question

Six points are placed on a circle. What is the greatest number of different lines that can be drawn so that each line passes through two of these points?

• A. $12$
• B. $15$
• C. $25$
• D. $30$
• E. $36$

Answer 1

Answer: (B)

$15$

There are six points on circle, we can draw a line with two points.

Among those six points, if we select any two different points then we will get a line.

Therefore number of different lines is equal to number of ways of selecting two points out of six points.

which is equal to ${}^6{C}_2=15$