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COMEDK2021MathematicsProbability

Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral equals

Options

  1. A1 2
  2. B1 5
  3. C1 10
  4. D1 20

Correct answer

C. 1 10

Step-by-step solution

The total number of ways to choose 3 vertices out of 6 is given by ⁶C₃ . ⁶C₃ = 6 5 4 3 2 1 = 20 . A regular hexagon has vertices labeled 1, 2, 3, 4, 5, 6 in order. A triangle formed by these vertices is equilateral if the indices of the vertices are in arithmetic progression with a common difference of 2. The possible sets of vertices are 1, 3, 5 and 2, 4, 6 . There are exactly 2 such triangles. The probability is the ratio of the number of favorable outcomes to the total number of outcomes: P = 2 20 = 1 10 . Answe

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