COMEDK · Maths · 36. Probability
Three vertices are chosen randomly from the seven vertices of a regular 7 -sided polygon. The probability that they form the vertices of an isosceles triangle is
- A \(\dfrac{1}{7}\)
- B \(\dfrac{1}{3}\)
- C \(\dfrac{3}{7}\)
- D \(\dfrac{3}{5}\)
Answer & Solution
Correct Answer
(D) \(\dfrac{3}{5}\)
Step-by-step Solution
Detailed explanation
The total number of ways to choose 3 vertices out of 7 is given by \(^{7}C_{3} = \dfrac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35\). An isosceles triangle is formed if at least two sides of the triangle are equal. In a regular 7-sided polygon, let the vertices be…
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