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

  • question_answer
    The number of ways in which 5 male and 2 female members of a committee can be seated around a round table so that the two female are not seated together is [Roorkee 1999]

    A) 480

    B) 600

    C) 720

    D) 840

    Correct Answer: A

    Solution :

    Fix up a male and the remaining 4 male can be seated in 4! ways.  Now no two female are to sit together and as such the 2 female are to be arranged in five empty seats between two consecutive male and number of arrangement will be\[{}^{5}{{P}_{2}}\]. Hence by fundamental theorem the total number of ways is = \[4!\,\,\times \,\,{}^{5}{{P}_{2}}\]  = 24 × 20 = 480 ways.


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