## Qustn frm qustn bank

. A, B, C and D are four towns, any three of which are non -collinear. The number of ways to construct three roads each joining a pair of towns so that the roads do not form a triangle is: (1)7 (2)8 (3)9 (4) more than 9 Q. A, B, C and D are four towns, any three of which are non -collinear. The number of ways to construct three roads each joining a pair of towns so that the roads do not form a triangle is: (1)7 (2)8 (3)9 (4)more than 9

## Solution:

Since the number of points is 4 and any 3 of them are non-collinear , the 4 points can be assumed to lie on a circle. The total number of roads that can be constructed using these 4 points is (4 C 2) = 4*3/2 = 6. Now we need to choose 3 roads out of these 6 roads which do not form a triangle. Number of ways to choose 3 roads forming triangle = 4. Total number of ways to choose 3 out of 6 roads = (6 C 3) = 20. Therefore required number of ways = 20 - 4 = 16 ( more than 9 ). ANS : (4)