Question

How many 7-digit phone numbers can be formed in the first digit cannot be 0, and any digit can be repeated?

Answer 1

This is an example of using an advanced counting scheme where we find the answer to be `9` million with out having to write them all out!!. Read on...

Explanation:

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 `1` through `9` and can be selected in nine different ways. Each remaining digit can then be selected in `10` ways, as zero can be used.

Since each digit choice is independent, we just multiply all these choices together:

`N = 9 xx 10 xx 10 xx 10 xx 10 xx 10 xx 10 = "9 million possibilities"`

(Shows you why area codes have to come into play.)