Question

A telephone company wants to create as many 7 digit phone numbers as possible without changing the first 3 digits. How many phone numbers can be created?

Answer 1

Assuming that repetitions are allowed:
The permutations available for the first 3 digits are
\[10^{3}\]
The permutations available for the last 4 digits are
\[10^{4}\]
Each of the 1000permutations of the first 3 digits can be taken with each of the number of permutations of the last 4 digits.
The total quantity of phone numbers that can be created is
\[10^{3}\times 10^{4}\]