If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is:

Question

Aicharya · Accepted Answer

Total number of ways of selecting three points from vertices of a regular hexagon

= {}^{6}{C_{3}} = \frac{6.5 . 4}{1.2 . 3} = 20

Favorable selection (forming equilateral triangle)

= 2 (ACE, BDF)

\Rightarrow

Required probability

P = \frac{N u m b e r o f f a v o u r a b l e s e l e c t i o n s}{T o t a l s e l e c t i o n s}

= \frac{2}{20} = \frac{1}{10}

If three of the six vertices of a regular hexagon are chosen at random, then the probability that the…

Solution