Question

There are 9 points in a plane out of which exactly 3 points are collinear, then

• A. Number of straight lines which can be formed by joining any of these 9 points is 34
• B. Number of triangles which can be formed by joining any 3 points out of these 9 points is 83
• C. Number of quadrilaterals which can be formed by joining any 4 points out of these 9 points is 120
• D. Number of triangles which can be formed by joining any 3 points out of these 9 points is 84

Answer 1

Answer: (A), (B)

A, B

Answer 2

1. Number of Straight Lines: Total lines = $\binom{9}{2} - \binom{3}{2} + 1 = 36 - 3 + 1 = 34$.

2. Number of Triangles: Total triangles = $\binom{9}{3} - \binom{3}{3} = 84 - 1 = 83$.

3. Number of Quadrilaterals: Total quadrilaterals = $\binom{9}{4} = 126$.

Options A and B are correct.