Question

Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C


Out of 6 vertices, 3 can be chosen in ${}^6{C}_3$ ways. The triangle will be equilateral if it is $\Delta ACEor\Delta BDF$ (2 ways).
Therefore, the required probability is
$\frac{2}{{}^6{C}_3}=\frac{2}{20}=\frac{1}{10}$