(b) 648
A number between 100 and 1000 has 3-digits
∴ Total number of 3-digit numbers having at least one of their digits as 7 = (Total number of 3-digit numbers) – (Total number of 3-digit numbers in which 7 does not appear at all)
(a) Total number of 3-digit numbers:
Clearly repetition of digits is allowed.
The hundred’s place can be filled in 9 ways, i.e., using any of the digits 1 to 9 excluding zero.
The ten’s and the unit’s place can be filled in 10 ways using all the digits from 0 – 9 in each place.
∴ Total number of 3-digit numbers = 9 × 10 × 10 = 900
(b) Total number of 3-digit numbers in which 7 does not appear at all:
Here, the digits to be used are 0, 1, 2, 3, 4, 5, 6, 8, 9 i.e., 9 in number.
Now, the hundred’s place can be filled in 8 ways (excluding 0), the tens’ and ones’ place can be filled in 9 ways each.
∴ Total number of 3-digit numbers in which 7 does not appear, = 8 × 9 × 9 = 648