### Instruction: How many different 7-digit positive integers exist? (Note that we don't allow "7-digit" integers that start with 0, such as 0123456; this is actually a 6-digit integer.).### Response: So for the first digit we have 9 choices, 1 through 9.
For the second digit we have 10 choices, 0 through 9.
Right. And for the third digit we have 10 choices.
And for the fourth digit we have 10 choices.
And for the fifth digit we have 10 choices.
And for the sixth digit we have 10 choices.
And for the seventh digit we have 10 choices.
So the total number of choices is $9 \cdot 10^6 = 9000000$.