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JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Definition of permutation, Number of permutations with or without repetition, Conditional permutations

  • question_answer
    The number of numbers that can be formed with the help of the digits 1, 2, 3, 4, 3, 2, 1  so that odd digits always occupy odd places, is       [RPET 1988, 1991, 1992]

    A) 24

    B) 18

    C) 12

    D) 30

    Correct Answer: B

    Solution :

    The 4 odd digits 1, 3, 3, 1 can be arranged in the 4 odd places in \[\frac{4\ !}{2\ !\ 2\ !}=6\] ways and 3 even digits 2, 4, 2 can be arranged in the three even places in \[\frac{3\ !}{2\ !}=3\] ways. Hence the required number of ways\[=6\times 3=18\].


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