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

  • question_answer
    20 persons are invited for a party. In how many different ways can they and the host be seated at a circular table, if the two particular persons are to be seated on either side of the host [IIT 1977]

    A) \[20\ !\]

    B) \[2\ .\ 18\ !\]

    C) \[18\ !\]

    D) None of these

    Correct Answer: B

    Solution :

    There are 20 + 1 = 21 persons in all. The two particular persons and the host be taken as one unit so that these remain 21 -  3 + 1 = 19 persons to be arranged in 18 ! ways. But the two person on either side of the host can themselves be arranged in 2! ways.  Hence there are 2 ! 18 ! ways  or \[2.18!\] ways.


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