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:

Step-by-step solution

Total number of ways of selecting three points from vertices of a regular hexagon =   C 3   6 = 6.5 . 4 1.2 . 3 = 20 Favorable selection (forming equilateral triangle) = 2   ACE ,   BDF ⇒ Required probability P = 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 = 2 20 = 1 10