Question

How many numbers are there between 100 and 1000 such that at least one of their digits is 7?

Answer 1

Numbers between $100$ and $1000=900$

Numbers between $100$ and $1000$ which do not have digit $7$ at any place $=8\times 9\times 9=648$
Here at hundred place, we have 8 possibilities as $0$ and $7$ can't be selected out of total $10$ digits.
at tense and units place there are $9$ possibilities as only $7$ can't be selected out of $10$ digits.

Therefore, numbers between $100$ and $1000$ which have at least one digit as $7=900-648=252$

Hence, there are $252$ numbers in between $100$ and $1000$ such that at least one of their digit is $7$.