JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Self Evaluation Test - Permutations and Combinatioins

  • question_answer
    From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangement is:

    A) At least 500 but less than 750

    B) At least 750 but less than 1000

    C) At least 1000

    D) Less than 500

    Correct Answer: C

    Solution :

    [c] 4 novels, out of 6 novels and 1 dictionary out of 3 can be selected in \[^{6}{{C}_{4}}{{\times }^{3}}{{C}_{1}}\] ways Then 4 novels with one dictionary in middle can be arranged in 4! Ways. \[\therefore \] Total ways of arrangement \[{{=}^{6}}{{C}_{4}}{{\times }^{3}}{{C}_{1}}\times 4!=1080\]


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