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JEE Main 2019 · 12 Apr · Shift I

JEE Main 2019 Mathematics question on Probability

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
  1. A.
    110\dfrac{1}{10}
  2. B.
    15\dfrac{1}{5}
  3. C.
    310\dfrac{3}{10}
  4. D.
    320\dfrac{3}{20}
Show answer and solution

Correct option: A

Solution

Total ways to choose 3 vertices from 6 is C(6,3) = 20.

In a regular hexagon, the only equilateral triangles are the two formed by alternate vertices: {1,3,5} and {2,4,6}.

So probability = 2/20 = 1/10.

[JEE Main 2019 · 12 Apr · Shift I]

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