question_answer

If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is:      [JEE Main Held on 12-4-2019 Morning]

A) \[\frac{3}{10}\]                                  

B) \[\frac{1}{10}\]

C) \[\frac{3}{20}\]                                  

D) \[\frac{1}{5}\]

Correct Answer: B

Solution :

Only two equilateral tringles are possible \[{{A}_{1}}{{A}_{3}}{{A}_{5}}\]and\[{{A}_{2}}{{A}_{5}}{{A}_{6}}\] \[\frac{2}{{{6}_{{{C}_{3}}}}}=\frac{2}{20}=\frac{1}{10}\]