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JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Self Evaluation Test - Permutations and Combinatioins

  • question_answer
    Two straight line intersect at a point O. Points \[{{A}_{1}},{{A}_{2}},...{{A}_{n}}\] are taken on one line and pints \[{{B}_{1}},{{B}_{2}},...,{{B}_{n}}\]on the other. If the point O is not to be used, the number of triangles that can be drawn using these points as vertices, is

    A) \[n(n-1)\]

    B) \[n{{(n-1)}^{2}}\]

    C) \[{{n}^{2}}(n-1)\]

    D) \[{{n}^{2}}{{(n-1)}^{2}}\]

    Correct Answer: C

    Solution :

    [c] No. of triangles \[{{=}^{2n}}{{C}_{3}}{{-}^{n}}{{C}_{3}}{{-}^{n}}{{C}_{3}}\] \[=\frac{2n(2n-1)(2n-2)}{6}-\frac{2n(n-1)(n-2)}{6}\] \[=\frac{1}{3}n(n-1)(3n)={{n}^{2}}(n-1).\]


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