A, B , C , and D are four towns, any three of which are non-collinear. Then, the number of ways to construct three roads each joining a pair of towns, so that the roads do not form a triangle, is?

To construct 2 roads, three towns can be selected out of 4 in 4 x 3 x 2 = 24 ways. Now, if third road goes from the third town to the first town, a triangle is formed and if it goes to the fourth town, a triangle is not formed, So there are 24 ways to form a triangle and 24 ways of avoiding the formation of triangle.