Q. Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with these three vertices is equilateral, equals
A) $\frac{1}{2}$
B) $\frac{1}{5}$
C) $\frac{1}{10}$
D) $\frac{1}{20}$
Explanation
(c)
We can choose three vertices out of 6 in ${\ ^{6}C}_{3} = 20$ ways. Chosen vertices can form an equilateral triangle in just two ways $viz,\ A_{1},A_{3},A_{5}\ and\ A_{2},A_{4},A_{6}$.
$\therefore\ \$Required probability $= \frac{2}{20} = \frac{1}{10}$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.