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BCECE Engineering BCECE Engineering Solved Paper-2004

  • question_answer
    There are six vertices of a regular hexagon are chosen at random, then the possibility that the triangle with three vertices is equilateral, is equal to:

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

    B)         \[\frac{1}{3}\]                  

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

    D)         \[\frac{1}{20}\]

    Correct Answer: C

    Solution :

    Key Idea: There are six equilateral triangle is formed in the regular hexagon. The total number of triangle formed by the six vertices \[={{\,}^{6}}{{C}_{3}}=20.\] The total number of equilateral triangles formed \[=6\] \[\therefore \] Required probability\[=\frac{2}{20}\]                                                 \[=\frac{1}{10}\]


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