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  4. Number of numbers from 1 to 2014 having atleast one digit 4 is

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Q. Number of numbers from 1 to 2014 having atleast one digit 4 is

Permutations and Combinations

Solution:

Single digit number containing no $4=8$
two digit number containing no $4=8 \cdot 9=72$
three digit number containing no $4=8 \times 9 \times 9=648$
four digit number containing no
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Starting with 2
$2000|1| 2|3| 5|6| 7|8| 9|10| 11|12| 13$
containing no 4 and less than $2014=13$
Total $=8+72+648+729+13=1470$
$\therefore $ Numbers containing atleast one $4=2014-1470=544$.