Q110 / 180 · COMEDK 2024 (Memory Based) · Mathematics
Three vertices are chosen randomly from the 10 vertices of a regular 10 sided polygon. The probability that they form the vertices of an isosceles triangle is
- A$\frac{4}{7}$
- B$\frac{3}{7}$
- C$\frac{4}{8}$
- Correct answerD$\frac{3}{8}$
Solution
Number of triangle formed $={ }^{10} C_3$
Number of isosceles triangle $=10\left(\frac{10-1}{2}\right)$
$=5 \times 9=45$
So, required
$\begin{aligned}<br/>\text { probability } & =\frac{45}{{ }^{10} C_3} \\<br/>& =\frac{45 \times 3 \times 2}{10 \times 9 \times 8}=\frac{3}{8}<br/>\end{aligned}$
Number of isosceles triangle $=10\left(\frac{10-1}{2}\right)$
$=5 \times 9=45$
So, required
$\begin{aligned}<br/>\text { probability } & =\frac{45}{{ }^{10} C_3} \\<br/>& =\frac{45 \times 3 \times 2}{10 \times 9 \times 8}=\frac{3}{8}<br/>\end{aligned}$
Hence, the correct answer is option: 'D'.