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Three of the 6 vertices of a regular hexagon are chosen at random.The probability that the triangle with these vertices is equilateral is
  • a)
    1/10
  • b)
    1/20
  • c)
    1/5
  • d)
    1/2
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Three of the 6 vertices of a regular hexagon are chosen at random.The ...
Rules of Triangle …..

Total possible cases = 6 C 3

Favourable cases =2

So the probability is = 2/6 C 3 =1/10.

Because there can be 2 22 equilateral triangles possible and total number of triangles possible would be (6/3) the answer is 1/10.
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Community Answer
Three of the 6 vertices of a regular hexagon are chosen at random.The ...
Let T represent the equilateral triangles
n(T)= No. if equilateral triangle, with six vertices ABCDEF of regular hexagon, are only two namely △ACE;△BDF
and n(S)= Total no. of triangles with six vertices are = 6C3 = 20
P(T) = n(T)/n(S) = 2/20 = 1/10
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Three of the 6 vertices of a regular hexagon are chosen at random.The probability that the triangle with these vertices is equilateral isa)1/10b)1/20c)1/5d)1/2Correct answer is option 'A'. Can you explain this answer?
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