COMEDK · Maths · 36. Probability
Three vertices are chosen randomly from the eight vertices of a regular 8-sided polygon. The probability that they form the vertices of an isosceles triangle, is
- A \(\dfrac{3}{7}\)
- B \(\dfrac{4}{7}\)
- C \(\dfrac{5}{7}\)
- D \(\dfrac{2}{7}\)
Answer & Solution
Correct Answer
(A) \(\dfrac{3}{7}\)
Step-by-step Solution
Detailed explanation
Total ways to choose 3 vertices from 8: \(\binom{8}{3} = 56\) For isosceles triangles, fix any vertex as the apex. For vertex 1, the symmetric pairs are \((2,8), (3,7), (4,6)\), giving 3 isosceles triangles per apex. Since 8 is not divisible by 3, no equilateral triangles exist,…
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