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

  • question_answer
    Numbers greater than 1000 but not greater than 4000 which can be formed with the digits 0, 1, 2, 3, 4  (repetition of digits is allowed), are [IIT 1976; AIEEE 2002]

    A) 350

    B) 375

    C) 450

    D) 576

    Correct Answer: B

    Solution :

    Numbers greater than 1000 and less than or equal to 4000 will be of 4 digits and will have either 1 (except 1000) or 2 or 3 in the first place with 0 in each of remaining places. After fixing \[{{1}^{st}}\] place, the second place can be filled by any of the 5 numbers. Similarly third place can be filled up in 5 ways and \[{{4}^{th}}\] place can be filled up in 5 ways. Thus there will be \[5\times 5\times 5=125\] ways in which 1 will be in first place but this include 1000 also hence there will be 124 numbers having 1 in the first place. Similarly 125 for each 2 or 3. One number will be in which 4 in the first place and \[i.e.\] 4000. Hence the required numbers are \[124+125+125+1=375\] ways.

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