Let 9 points lie on the line y = 2x and 12 points on the y = x/2 in the first quadrant.

Question

Let 9 points lie on the line y = 2x and 12 points on the \(y=\frac{x}{2}\) in the first quadrant. Find the number of triangles formed using these points and origin.

(1) 1134

(2) 1096

(3) 1120

(4) 1026

Answer 1

Correct option is: (1) 1134 

Total triangles : (two points of y = 2x, 1 point of \(y=\frac{x}{2}\)) + (two points on \(y=\frac{x}{2},\) 1 point of y = 2x) + (1 point on y = 2x, 1 point of \(y=\frac{x}{2}\) and origin)

\(={ }^{9} C_{2} \cdot{ }^{12} C_{1}+{ }^{9} C_{1} \cdot{ }^{12} C_{2}+{ }^{1} C_{1} \cdot{ }^{9} C_{1} \cdot{ }^{12} C_{1}\)    

= 1134