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

  • question_answer
    If \[^{15}{{C}_{3r}}{{=}^{15}}{{C}_{r+3}}\], then the value of \[r\] is [IIT 1967; RPET 1991; MP PET 1998; Karnataka CET 1996]

    A) 3

    B) 4

    C) 5

    D) 8

    Correct Answer: A

    Solution :

    \[^{15}{{C}_{3r}}{{=}^{15}}{{C}_{r+3}}{{\Rightarrow }^{15}}{{C}_{15-3r}}{{=}^{15}}{{C}_{r+3}}\] \[\Rightarrow 15-3r=r+3\Rightarrow r=3\].


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