JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Multinomial Theorem, Number of Divisors, Miscellaneous problems

  • question_answer
    An n-digit number is a positive number with exactly \[n\] digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2, 5 and 7. The smallest value of \[n\] for which this is possible is [IIT 1998]

    A) 6

    B) 7

    C) 8

    D) 9

    Correct Answer: B

    Solution :

    Since at any place, any of the digits 2, 5 and 7 can be used, total number of such positive \[n\]-digit numbers are \[{{3}^{n}}\]. Since we have to form 900 distinct numbers, hence\[{{3}^{n}}\ge 900\Rightarrow n=7\].


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