Deleted - just one question per post thanks.
3) How many positive integers less than 1000 have at least one digit of 0?
10 *9 + 9 = 99 have an ending digit of 0
9*9 = 81 have a middle digit of 0 [ but not an ending digit of 0 ]
So
99 + 81 = 180 have at least one 0
1 digit number = 0 cases
2 digit number = 9 x 1 = 9
3 digit number : 9 x 9 x 1 + 9 x 1 x 9 + 9 x 1 x 1 = 171
Finally, add 1000 as last number.
Total numbers containing 0 as one of its digits = 0 + 9 + 171 + 1 = 181.
EP: The question says "Less than a 1000". So, Cphill's answer is correct.
+128474 
