If three 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

# If three 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

1. A

1/10

2. B

3/10

3. C

1/5

4. D

3/20

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### Solution:

Choosing three vertices of a regular hexagon alternately, only two equilateral triangles are possible,

i.e., ${A}_{1},{A}_{3},{A}_{5}$ and ${A}_{2},{A}_{4},{A}_{6}$ Hence,

required probability=

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