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

  • question_answer
    If \[^{8}{{C}_{r}}{{=}^{8}}{{C}_{r+2}}\], then the value of \[^{r}{{C}_{2}}\] is [MP PET 1984; RPET 1987]

    A) 8

    B) 3

    C) 5

    D) 2

    Correct Answer: B

    Solution :

    \[^{8}{{C}_{r}}{{=}^{8}}{{C}_{r+2}}\Rightarrow 8-r=r+2\Rightarrow r=3\] Hence\[^{3}{{C}_{2}}=3\].


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