JEE Main & Advanced Mathematics Probability Question Bank Use of permutations and combinations in probability

  • question_answer
    Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with these three vertices is equilateral, is equal to [IIT 1995; MP PET 2002, 04]

    A)            \[\frac{1}{2}\]                          

    B)            \[\frac{1}{5}\]

    C)            \[\frac{1}{10}\]                       

    D)            \[\frac{1}{20}\]

    Correct Answer: C

    Solution :

                       Total number of triangles which can be formed is equal to \[{}^{6}{{C}_{3}}=\frac{6\times 5\times 4}{1\times 2\times 3}=20\]                    Number of equilateral triangles = 2                    \[\therefore \] Required probability \[=\frac{2}{20}=\frac{1}{10}.\]


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