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Q. The number of times the digit $0$ is used in writing the numbers from $1$ to $1000$ is equal to

NTA AbhyasNTA Abhyas 2020Permutations and Combinations

Solution:

Consider the number from $000, \, 001, \, 002,....., \, 998, \, 999.$
Since, each digit has an equal likelihood of coming and digits used are $3\times 1000.$
Hence, 0 appears $=300$ times
But, $000,001,002,....,098,099;$
have some unwanted zeros, we subtract
these zero’s i.e. $3\times 1+2\times 9+1\times 90=111.$
Thus, total times 0 appears $=300-111=189$
Also, add $3$ zero’s in 1000.
$\Rightarrow 189+3=192.$