Question

Two straight lines intersect at a point O. Points $A_1,A_2,A_3,A_4,A_5,...,A_m$ are taken on one line and points $B_1,B_2,B_3,....,B_n$ on the other. If the point O is not included, the number of triangles that can be drawn using these points as vertices is:

• A. ${}^n{C}_2{+}^m{C}_2$
  
• B. ${}^{2n}{C}_2$
  
• C. ${}^{m+n}{C}_2$
• D. None of these

Answer 1

The correct option is D None of these

Required number of triangles =${}^{m+n}{C}_3{-}^m{C}_3{-}^n{C}_3.$