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

  • question_answer
    In how many ways can 6 persons be selected from 4 officers and 8 constables, if at least one officer is to be included   [Roorkee 1985; MP PET 2001]

    A) 224

    B) 672

    C) 896

    D) None of these

    Correct Answer: C

    Solution :

    Required number of ways \[{{=}^{4}}{{C}_{1}}{{\times }^{8}}{{C}_{5}}{{+}^{4}}{{C}_{2}}{{\times }^{8}}{{C}_{4}}{{+}^{4}}{{C}_{3}}{{\times }^{8}}{{C}_{3}}{{+}^{4}}{{C}_{4}}{{\times }^{8}}{{C}_{2}}\] \[=4\times 56+6\times 70+4\times 56+1\times 28=896\].


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