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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 \[^{n}{{C}_{r}}=84,{{\ }^{n}}{{C}_{r-1}}=36\] and \[^{n}{{C}_{r+1}}=126\], then \[n\] equals [RPET 1997; MP PET 2001]

    A) 8

    B) 9

    C) 10

    D) 5

    Correct Answer: B

    Solution :

    \[\frac{n-r+1}{r}=\frac{84}{36}=\frac{7}{3}\] and \[\frac{n-r}{r+1}=\frac{126}{84}=\frac{3}{2}\] \[\therefore \]\[\frac{7}{3}r-1=n-r=\frac{3}{2}(r+1)\] or \[14r-6=9r+9\]  or \[r=3\].  So, \[n=9\].


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