Q89 / 180 · COMEDK 2023 (Memory Based) · Mathematics

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

  • A
    $\frac{4}{7}$
  • Correct answer
    B
    $\frac{3}{7}$
  • C
    $\frac{2}{7}$
  • D
    $\frac{5}{7}$

Solution

Number of triangles formed $={ }^9 C_3$ Number of isosceles triangles $=9 \times\left(\frac{9-1}{2}\right)$ $=9 \times 4=36$ So, required probability $=\frac{36}{{ }^9 C_3}=\frac{36}{\frac{9 !}{3 !(9-3) !}}=\frac{36 \times 3 \times 2 \times 6 !}{9 \times 8 \times 7 \times 6 !}=\frac{3}{7}$

Hence, the correct answer is option: 'B'.

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