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Question

If three vertices of a regular hexagon are chosen at random, then the chance that they form an equilateral triangle is


A

13

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B

15

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C

110

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D

12

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Solution

The correct option is C

110


Explanation for the correct option:

Finding the probability of an equilateral triangle:

ABCDEF is a regular hexagon.

Total number of triangles =6C3

=6!3!3![nCr=n!r!n-r!]=20

The only equilateral triangle possible are ACE and BDF from three vertices as shown in figure.

Therefore, the required probability is

=2C36=220=110

Hence, the correct option is C.


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