Question

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 :

• A. $\frac{1}{10}$
• B. $\frac{1}{5}$
• C. $\frac{3}{10}$
• D. $\frac{3}{20}$

Answer 1

The correct option is A $\frac{1}{10}$

Number of total triangle $={}^6{C}_3=20$
Number equilateral triangle $=2$


Required Probability$=\frac{2}{20}=\frac{1}{10}$