Question

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

• A. $1/2$
• B. $1/5$
• C. $1/10$
• D. $1/20$

Answer 1

Answer: (C)

$1/10$

Total number of triangles which can be formed is equal to ${}^6{C}_3=\frac{6\times 5\times 4}{1\times 2\times 3}=20$
Number of equilateral triangles $=2$
$\therefore$ Required probability $=\frac{2}{20}=\frac{1}{10}$