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

  • question_answer
    The number of ways in which 10 persons can go in two boats so that there may be 5 on each boat, supposing that two particular persons will not go in the same boat is [Pb. CET 1999]

    A) \[\frac{1}{2}{{(}^{10}}{{C}_{5}})\]

    B) \[2{{(}^{8}}{{C}_{4}})\]

    C) \[\frac{1}{2}{{(}^{8}}{{C}_{5}})\]

    D) None of these

    Correct Answer: B

    Solution :

    First omit two particular persons, remaining 8 persons may be 4 in each boat. This can be done in \[^{8}{{C}_{4}}\] ways. The two particular persons may be placed in two ways one in each boat. Therefore total number of ways are\[=2{{\times }^{8}}{{C}_{4}}\].


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