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

  • question_answer
    If \[^{2n}{{C}_{2}}{{:}^{n}}{{C}_{2}}=9:2\] and \[^{n}{{C}_{r}}=10\], then \[r=\]

    A) 1

    B) 2

    C) 4

    D) 5

    Correct Answer: B

    Solution :

    \[\left( \frac{(2n)\ !}{2\ !\ (2n-2)\ !} \right)\,\,2=\left( \frac{n\ !}{2\ !(n-2)\ !} \right)\,\,9\] \[\Rightarrow (2n)(2n-1)2=9n(n-1)\Rightarrow n=5\] Now\[^{5}{{C}_{r}}=10\Rightarrow r=2\].


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