JEE Main & Advanced
JEE Main Paper (Held on 12-4-2019 Morning)
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\[{{A}_{2}}{{A}_{5}}{{A}_{6}}\] \[\frac{2}{{{6}_{{{C}_{3}}}}}=\frac{2}{20}=\frac{1}{10}\]