SOLUTION: How many integers from 3000 to 8999 inclusive contain no 7's? ( Answer should be 3645) Thank you!

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Question 873516: How many integers from 3000 to 8999 inclusive contain no 7's? ( Answer should be 3645)
Thank you!
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
For the thousands digit you can choose 3,4,5,6,or 8.
That's 5 choices>
for each of the other places (hundreds, tens, and ones), you can pick any digit except 7.
That is 9 choices for each digit.
The choices multiply tree-style, because for each choice for the thousands place you have 9 choices for the hundreds place,
making 5%2A9=45 choices for the first two digits, and so on.
The total number of choices is
5%2A9%2A9%2A9=5%2A81%2A9=5%2A729=3645