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.)

1 Answer
Geoff K.
May 8, 2018

There are 9,000,000 seven-digit positive integers.

Explanation:

For the first digit, we have 9 choices: 1, 2, 3, 4, 5, 6, 7, 8, 9.
For each remaining digit, we have 10 choices: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Each choice is independent of the others. So, the number of total 7-digit positive integers is the product of all the numbers of choices for each digit.

In other words:

#9 xx 10 xx 10 xx 10 xx 10 xx 10 xx 10#

#"= 9,000,000"#

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