JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Critical Thinking Questions

  • question_answer There are three girls in a class of 10 students. The number of different ways in which they can be seated in a row such that no two of the three girls are together is

    A) \[7\ !\ {{\times }^{6}}{{P}_{3}}\]

    B) \[7\ !\ {{\times }^{8}}{{P}_{3}}\]

    C) \[7\ !\ \times 3\ !\]

    D) \[\frac{10\ !}{3\ !\ 7\ !}\]

    Correct Answer: B

    Solution :

    Seven boys can be seated in a row in \[7\ !\] ways. Hence the total no. of arrangement such that no two girls seated together\[=7\ !\ {{\times }^{8}}{{P}_{3}}\].

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