JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Circular Permutations

  • question_answer
    In how many ways can 5 boys and 5 girls sit in a circle so that no two boys sit together [IIT 1975; MP PET 1987]

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

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

    C) \[\frac{5\,\,!\,\,\times \,\,5\,\,!}{2}\]

    D) None of these

    Correct Answer: B

    Solution :

    Since total number of ways in which boys can occupy any place is \[(5-1)\ !=4\ !\] and the 5 girls can be sit accordingly in \[5\ !\] ways. Hence required number of ways are\[4\ !\ \times 5\ !\].


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