Question

There are $10$ points in a plane.Of these ten points four points are in a straight line and with the exception of these four points no other three points are in the same straight line. Find the number of quadrilaterals formed by joining these points.

• A. $155$
• B. $200$
• C. $125$
• D. $185$

Answer 1

The correct option is D $185$

$10$ Points , $4$ are collinear

Number of Quadrilatrals

${=}^6{C}_4{+}^6{C}_3{\times }^4{C}_1{+}^6{C}_2{\times }^4{C}_2$

$=15+80+90$

$=185$ Quadrilatrals

Therefore Number of Quadrilatrals $=185$