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COMEDK2023MathematicsProbability

Three vertices are chosen randomly from the nine vertices of a regular 9 -sided polygon. The probability that they form the vertices of an isosceles triangle, is

Options

  1. A4 7
  2. B3 7
  3. C2 7
  4. D5 7

Correct answer

B. 3 7

Step-by-step solution

Number of triangles formed = ^9 C₃ Number of isosceles triangles =9 ( 9-1 2 )=9 4=36 So, required probability = 36 ^9 C₃ = 36 9 ! 3 !(9-3) ! = 36 3 2 6 ! 9 8 7 6 ! = 3 7

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