JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Critical Thinking Questions

  • question_answer How many numbers lying between 10 and 1000 can be formed from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 (repetition is allowed)

    A) 1024

    B) 810

    C) 2346

    D) None of these

    Correct Answer: B

    Solution :

    The total number between 10 and 1000 are 989 but we have to form the numbers by using numerals \[1,\ 2,........9,\ \ i.e.\]0 is not occuring so the numbers containing any ?0? would be excluded i.e., Required number of ways \[=989-\left\{ \begin{align}   & 20,\ 30,\ 40,................100=9 \\  & 101,\ 102,...................200=19 \\  & 201,........................300=19 \\  & ............................................. \\  & ............................................. \\  & 901,..........................990=18 \\ \end{align} \right\}\] \[=989-(9+18+19\times 8)=810\]. Aliter: Between 10 and 1000, the numbers are of 2 digits and 3 digits. Since repetition is allowed, so each digit can be filled in 9 ways. Therefore number of 2 digit numbers \[=9\times 9=81\] and number of 3 digit numbers \[9\times 9\times 9=729\] Hence total ways\[=81+729=810\].


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