Question

How many triangles can be formed from $12$ points out of which $6$ points are collinear?

• A. $200$
• B. $120$
• C. $320$
• D. $400$

Answer 1

The correct option is A $200$

There are $12$ points of which $6$ are collinear points.

Case 1 : Take any $3$ points form $6$ non -collinear points.

Number of triangles ${=}^6{c}_3=20$

Case 2: Take any $1$ point from $6$ collinear points and $2$ from non -collinear points.

Number of triangles ${=}^6{c}_1{\times }^6{c}_2=15\times 6=90$

Case 3 take $2$ points from collinear points and $1$ from non -collinear points .

${=}^6{C}_2{\times }^6{c}_1=90$

Total $=200$