Question

Two lines intersect at O. Points $A_1,A_2,....A_n$ are taken on one of them and $B_1,B_2,...B_n$ on the other. The number of triangles that can be drawn with the help of these (2n+1) points is:

• A. n
• B. $n^2$
• C. $n^3$
• D. $n^4$

Answer 1

The correct option is C $n^3$

Required number of triangles $={(}^{2n}{C}_3{-}^n{C}_3{-}^n{C}_3)+(n\times n)=n^2(n-1)+n^2=n^3$
Alternatively :Required number of triangles
$={(}^n{C}_2{\times }^n{C}_1)+{(}^n{C}_1{\times }^n{C}_2)+(n\times n)=n^3$