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

  • question_answer
    The total number of 3-digit numbers, the sum of whose digits is even, is equal to

    A) 450

    B) 350

    C) 250

    D) 325

    Correct Answer: A

    Solution :

    [a] Let the number be \[n=pqr.\] As \[p+q+r\] is even, there are following cases: (i) p, q, r all are even \[\to 4.5.5=100\] ways (ii) p even and q, r are odd \[\to 4.5.5=100\]ways (iii) p odd, q and r even \[\to 5.5.5=125\]ways (iv) p odd, q even, r odd\[\to 5.5.5=125\] Total ways \[=100+100+125+125=450.\]

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