COMEDK · Maths · 36. Probability
Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral equals
- A \(\dfrac{1}{2}\)
- B \(\dfrac{1}{5}\)
- C \(\dfrac{1}{10}\)
- D \(\dfrac{1}{20}\)
Answer & Solution
Correct Answer
(C) \(\dfrac{1}{10}\)
Step-by-step Solution
Detailed explanation
The total number of ways to choose 3 vertices out of 6 is given by \(^{6}C_{3}\). \(^{6}C_{3} = \dfrac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20\). A regular hexagon has vertices labeled \(1, 2, 3, 4, 5, 6\) in order. A triangle formed by these vertices is equilateral if…
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