SOLUTION: how many whole numbers between 1 and 1,000 do not contain the digit 1?

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Question 766794: how many whole numbers between 1 and 1,000 do not contain the digit 1?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Obviously our number can't be 1000, so the maximum possible number of digits is 3.
If our number is a one+digit number, then there are eight possibilities: 2 to 9.
If our number is a two+digit number, there are 8 possibilities for the tens digit (anything but 0 and 1) and 9 possibilities for the units digit for a total of 8%2A+9+=+72 numbers.
If our number is a three+digit number, there are 8 possibilities for the hundreds digit and 9 possibilities for the tens and 9 for the units digits for a total of 8+%2A+9%2A+9+=+648.
So, the total is 648+%2B+72+%2B+8+=+728.