Question

There are 10 points and out of which 4 are collinear. How different triangle can be made using 10 points.

• A. ${}^{10}{C}_3{-}^3{C}_3$
• B. ${}^9{C}_3{-}^2{C}_2$
• C. ${}^{10}{C}_3{-}^4{C}_3$
• D. ${}^{10}{C}_3{-}^5{C}_3$

Answer 1

The correct option is C ${}^{10}{C}_3{-}^4{C}_3$

To make a triangle we need 3 non-collinear point
$\Rightarrow$ Out 10, 3 points can be selected in

${}^{10}{C}_{3}waysbut,thisselection$ ${}^4{C}_{3}selection$ are also included but these 4 points are collinear hence total number of feasible triangles,
${=}^{10}{C}_3{-}^4{C}_{3}Option\left(c\right)$