Question

There are $8$ points in a plane out of which $4$ are collinear. How many triangles can be formed with these these points as vertices?

• A. $52$
• B. $56$
• C. $48$
• D. $54$

Answer 1

The correct option is A $52$

There are $4$ points collinear. There would be $3$ cases

1. Choose any three points from $4$ non - collinear points.

2. Choose any $2$ points from $4$ non collinear and $1$ point from collinear points.

3. Choose any $2$ points from $4$ collinear and $1$ point from non -collinear points.

Total number of ways ${=}^4{C}_3$ ${+}^4{C}_1{\times }^4{C}_2$ + $4_1^C{\times }^4{C}_2$

$=52$