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 3 girls sit in a row so that no two girls are together

    A) \[5\,\,!\,\,\times \,\,3\,\,!\]

    B) \[^{4}{{P}_{3}}\times 5\,\,!\]

    C) \[^{6}{{P}_{3}}\times 5\,\,!\]

    D) \[^{5}{{P}_{3}}\times 3\,!\]

    Correct Answer: C

    Solution :

    Since the 5 boys can sit in \[5\ !\] ways. In this case there are 6 places are vacant in which the girls can sit in \[^{6}{{P}_{3}}\] ways. Therefore required number of ways are\[^{6}{{P}_{3}}\times 5\ !\].

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