Numbers between 99 and 1000 are all three-digit numbers.
Total number of 3 digit numbers having at least one of their digits as 7 = (Total numbers of three-digit numbers) – (Total number of 3 digit numbers in which 7 does not appear at all)
= (9 × 10 × 10) – (8 × 9 × 9)
= 900 – 648
= 252