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

  • question_answer
    The sum of all 4 digit numbers that can be formed by using the digits 2, 4, 6, 8 (repetition of digits not allowed) is

    A) 133320

    B) 533280

    C) 53328

    D) None of these

    Correct Answer: A

    Solution :

    Sum of the digits in the unit place is \[6(2+4+6+8)=120\] units. Similarly, sum of digits in ten place is 120 tens and in hundredth place is 120 hundreds etc. Sum of all the 24 numbers is \[120(1+10+{{10}^{2}}+{{10}^{3}})=120\times 1111=133320\].

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