(i) How many numbers are there between 99 and 1000 having 7 in the units place?

(ii) How many numbers are there between 99 and 1000 having at least one of their digits 7?

(i) First note that all these numbers have three digits. 7 is in the unit’s place. The middle digit can be any one of the 10 digits from 0 to 9. The digit in hundred’s place can be any one of the 9 digits from 1 to 9. Therefore, by the fundamental principle of counting, there are 10 × 9 = 90 numbers between 99 and 1000 having 7 in the unit’s place.

(ii) 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.