Question

The number of numbers between $1$ and ${10}^{10}$ which contain the digit $1$ is

• A. ${10}^{10}-9^{10}+1$
• B. ${10}^{10}-9^{10}-1$
• C. ${10}^{10}-8^{10}+1$
• D. ${10}^{10}-9^{10}+2$

Answer 1

The correct option is A ${10}^{10}-9^{10}+1$

Total number of $10$ digits numbers$={10}^{10}$

Total number of $10$ digits numbers without $1=9^{10}$

Total number of $10$ digits numbers Containing $1={10}^{10}-9^{10}$

$1$ extra count for ${10}^{10}$ itself.

$\therefore$ Total number of numbers between $1$ and ${10}^{10}$ is ${10}^{10}-9^{10}+1$