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 4 digit numbers that can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7 so that each number contain digit 1 is [AMU 2001]

    A) 1225

    B) 1252

    C) 1522

    D) 480

    Correct Answer: D

    Solution :

    After fixing 1 at one position out of 4 places 3 places can be filled by \[^{7}{{P}_{3}}\] ways. But some numbers whose fourth digit is zero, so such type of ways  = \[^{6}{{P}_{2}}\] \  Total ways = \[^{7}{{P}_{3}}\,-{{\,}^{6}}{{P}_{2}}\,=\,480\].


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