## Math problem

5. There are 4 towns, three of which are non-collinear. Then, the number of ways to construct 3 roads ach road joining a pair of towns so that the roads do not form a triangle is: a)9 b)12 c)16 d)24 Thanks in advance

## To construct 2 roads, three

To construct 2 roads, three towns can be selected out of 4 in 4 *3 *2 = 24 ways. Now if join 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 a triangle. Later I will explain it in details