In a plane, there are 9 points, out of which 4 are collinear. The number of triangles made by these points is:

80

The correct answer is Option (1) → 80

Step 1: Total triangles if no 3 points are collinear

$\text{Total triangles} = \begin{pmatrix}9\\3\end{pmatrix} = \frac{9 \cdot 8 \cdot 7}{3 \cdot 2 \cdot 1} = 84$

Step 2: Subtract triangles formed by collinear points

• Triangles cannot be formed by 3 points lying on the same line.
• Number of triangles among 4 collinear points:

$\begin{pmatrix}4\\3\end{pmatrix} = 4$

Step 3: Total valid triangles

$\text{Valid triangles} = 84 - 4 = 80$