CAT Quantitative Ability Questions | CAT Permutation, Combination and Probability questions
CAT/1995
Question . 65
A,B,C and D are four towns any three of which are non-colinear. 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
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Explanatory Answer
Method of solving this CAT Quantitative Ability Question from Permutation, Combination and Probability question
(d) To construct 2 roads, three towns can be selected out of 4 in 4 ×3×2 = 24 ways.
Now if the 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 a triangle.