Question

If three vertices of a regular hexagon are chosen at random, then he chance that they form an equilateral triangle is

• A. $\frac{1}{3}$
• B. $\frac{1}{5}$
• C. $\frac{1}{10}$
• D. $\frac{1}{2}$

Answer 1

Answer: (C)

$\frac{1}{10}$

Three vertices can be selected in ${}^6{C}_3$ ways.
The only equilateral triangles possible are $A_1{A}_3{A}_5$ and $A_2{A}_4{A}_6$
$p=\frac{2}{{}^6{C}_3}=\frac{2}{20}=\frac{1}{10}$.