If three vertices of a regular hexagon are chosen at random,... | Mathematics | SolveeIt | Solveeit

Today, August 18

Question

If three vertices of a regular hexagon are chosen at random, then the 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

$\frac{1}{10}$

Explanation

Solution

Three vertices can be selected in $^{6}C_{3}$ ways.
The only equilateral triangles possible are
$A_1A_3A_5$ and $A_2A_4A_6$
$p = \frac{2}{^{6}C_{3}} = \frac{2}{20} = \frac{1}{10}$