JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Self Evaluation Test - Permutations and Combinatioins

  • question_answer
    How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places?

    A) 18

    B) 28

    C) 6

    D) 27

    Correct Answer: A

    Solution :

    [a] There are 4 odd digits (1, 1, 3, 3) and 4 odd place (first, third, fifth and seventh). At these places the odd digits can be arranged in \[\frac{4!}{2!2!}\]=6 ways Then at the remaining 3 places, the remaining three digits (2, 2, 4) can be arranged in \[\frac{3!}{2!}=3\] ways \[\therefore \] The required of number of numbers \[=6\times 3=18\]


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