Probability 1 Question 3

3. If there of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is

(a) 110

(b) 15

(c) 310

(d) 320

(2019 Main, 12 April I)

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Answer:

Correct Answer: 3. (a)

Solution:

  1. Since, there is a regular hexagon, then the number of ways of choosing three vertices is 6C3. And, there is only two ways i.e. choosing vertices of a regular hexagon alternate, here A1,A3,A5 or A2,A4,A6 will result in an equilateral triangle.

Required probability

=26C3=26!3!3!=2×3×2×3×26×5×4×3×2×1=110



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