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

  • question_answer
    All possible four digit numbers are formed using the digits 0, 1, 2, 3 so that no number has repeated digits. The number of even numbers among them is

    A) 9

    B) 18

    C) 10

    D) None of these

    Correct Answer: C

    Solution :

    In forming even numbers, the position on the right can be filled either 0 or 2. When 0 is filled, the remaining positions can be filled in \[3\ !\] ways and when 2 is filled, the position on the left can be filled in 2 ways (0 cannot be used) and the middle two positions in \[2\ !\] ways (0 can be used). Therefore the number of even numbers formed \[=3\ !+2(2\ !)=10\].

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