Multiple choice

If three vertices of a regular hexagon are chosen at random, then he chance that they form an equilateral triangle is

  1. $\dfrac {1}{3}$
  2. $\dfrac {1}{5}$
  3. $\dfrac {1}{10}$
  4. $\dfrac {1}{2}$
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C Correct answer
Explanation

A regular hexagon has 6 vertices. The total number of ways to choose 3 vertices is 6C3 = 20. There are only 2 sets of vertices that form an equilateral triangle (the two sets of alternating vertices). Thus, the probability is 2/20 = 1/10.

AI explanation

The total number of ways to choose 3 vertices from a regular hexagon is given by the combination formula 6C3, which equals 20. A regular hexagon contains exactly 2 equilateral triangles formed by alternating vertices. The required probability is 2 divided by 20, which simplifies to 1/10.

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