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  4. Three of the six vertices of a regular hexagon are chosen at rondom. The probability that the triangle with three vertices is equilateral, equals

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Q. Three of the six vertices of a regular hexagon are chosen at rondom. The probability that the triangle with three vertices is equilateral, equals

IIT JEEIIT JEE 1995Probability

Solution:

Three vertices out of $6$ can be chosen in ${}^6C_3$ ways
So, total ways $={}^6C_3 =20$
Only two equilateral triangles can be formed
$\Delta AEC$ and $\Delta BFD$
image
$\therefore $ Favourable ways $= 2$
So, required probability = $\frac{2}{20}=\frac{1}{10}$