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

  • question_answer
    If  \[^{10}{{C}_{r}}{{=}^{10}}{{C}_{r+2}}\], then  \[^{5}{{C}_{r}}\] equals [RPET 1996]

    A) 120

    B) 10

    C) 360

    D) 5

    Correct Answer: D

    Solution :

    \[^{10}{{C}_{r}}{{=}^{10}}{{C}_{r+2}}\Rightarrow r+r+2=10\Rightarrow r=4\] \[\therefore \]\[^{5}{{C}_{r}}{{=}^{5}}{{C}_{4}}=\frac{5\ !}{1\ !\ 4\ !}=5\].


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