Question

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

• A. $\frac{1}{2}$
• B. $\frac{1}{5}$
• C. $\frac{1}{10}$
• D. $\frac{1}{20}$

Answer 1

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

We can choose vertices out of 6 in ${}^6{C}_3=20$ ways

Chosen vertices can form an equilateral triangle in just two ways namely $A_1{A}_3{A}_5$ and $A_2{A}_4{A}_6$

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