JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Definition of combinations, Conditional combinations, Division into groups, Derangements

  • question_answer
    If \[^{n}{{C}_{12}}={{\,}^{n}}{{C}_{6}}\], then \[^{n}{{C}_{2}}=\] [Karnataka CET 2005]

    A) 72

    B) 153

    C) 306

    D) 2556

    Correct Answer: B

    Solution :

    Given \[{{\,}^{n}}{{C}_{12}}={{\,}^{n}}{{C}_{6}}\] \\[12+6=n\Rightarrow n=18\] \\[^{18}{{C}_{2}}=\frac{18\times 17}{2}=9\times 17=153\].


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