Question

What is the maximum possible number of intersection points of 15 lines in a plane, assuming no two lines are parallel and no three are concurrent?

• A. 105
• B. 210
• C. 91
• D. 120

Hint:

Use combination formula \( \binom{n}{2} \) for intersection points when no two lines are parallel and no three concurrent.

Answer 1

The Correct Option is A

Maximum number of intersection points from \( n \) lines, no two parallel, no three concurrent: \[ \text{Maximum} = \binom{n}{2} = \frac{n(n - 1)}{2} \] So, \[ \binom{15}{2} = \frac{15 14}{2} = \boxed{105} \]