Question

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

Answer 1

The correct option is B

$810$

Explanation for the correct option:

Total number of digits $\left(1,2,3,4,5,6,7,8,9\right)$ $=$ $9$

Since the repetition is allowed,

Total number of two digit numbers can be formed $=$ $9\times 9$ $=$ $81$

Total number of three digit numbers can be formed $=$ $9\times 9\times 9$ $=$ $729$

Total numbers can be formed $=$ $81+729$$=$ $810$

Therefore, total numbers formed from $10$ to $1000$ with the digits $\left(1,2,3,4,5,6,7,8,9\right)$ $=$ $810$

Hence, option $\text{'B'}$ is correct.