Three of six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral equal to :
Step-by-Step Solution
Key Concept: Recognize that equilateral triangles cannot be formed from collinear points except in special degenerate cases.
Total ways to choose 5 points from 5 collinear points is $^5C_5 = 20$. For an equilateral triangle, all three vertices must be non-collinear, but choosing from 5 collinear points permits only degenerate triangles. Only 2 configurations yield an equilateral triangle. Required probability is $\frac{2}{20} = \frac{1}{10}$.
Correct Answer: 3