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The number of numbers between 1 and $10^{10},$ $(e x c l u d i n g 1 a n d 10^{10})$ which contains digit 1 is

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$10^{10} - 9^{10}$

$10^{10} - 9^{10} - 1$

$10^{9}$

${\sum_{r = 0}^{10}}^{10} C_{r} 9^{r}$

answer is B.

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Detailed Solution

I II III X
Total number of numbers = $10^{10}$
Total number of numbers = $9^{10}$ (when we do not use = 1)
Total number of numbers $S = 1$ (when we use only)

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