How many 7-digit phone numbers can be formed in the first digit cannot be 0, and any digit can be repeated?
This is an example of using an advanced counting scheme where we find the answer to be
We consider that each digit is selected independently of the others. This is a consequence of the statement that says digits can be repeated.
The first digit can be any of
Since each digit choice is independent, we just multiply all these choices together:
(Shows you why area codes have to come into play.)