JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Definition of permutation, Number of permutations with or without repetition, Conditional permutations

  • question_answer
    In how many ways can 5 boys and 5 girls stand in a row so that no two girls may be together [RPET 1997]

    A) \[{{(5\ !)}^{2}}\]

    B) \[5\ !\ \times 4\ !\]

    C) \[5\ !\ \times 6\ !\]

    D) \[6\times 5\ !\]

    Correct Answer: C

    Solution :

    5 boys can be stand in a row \[5\ !\] ways Now, two girls can't stand in a row together in \[^{6}{{P}_{5}}\] ways. Total no. of required arrangement\[=5\ !\ {{\times }^{6}}{{P}_{5}}=5\ !\ \times 6\ !\].


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