SOLUTION: A social security number consists of nine digits. How many different Social Security numbers are possible if repetition is permitted?

First way:

Obviously there are 999999999 social security numbers in this list:

000-00-0001
000-00-0002
...........
...........
...........
999-99-9997
999-99-9998
999-99-9999

For that's the same as counting for 1 to 999999999.

But there is one more not in the list, namely 000-00-0000.
So there are 1000000000 or 1 billion social security numbers.

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A second way to do it is this way:

Suppose a social security number is 

ABC-DE-FGHI

There are 10 choices for a digit to go in the A position
There are 10 choices for a digit to go in the B position
There are 10 choices for a digit to go in the C position
There are 10 choices for a digit to go in the D position
There are 10 choices for a digit to go in the E position
There are 10 choices for a digit to go in the F position
There are 10 choices for a digit to go in the G position
There are 10 choices for a digit to go in the H position
There are 10 choices for a digit to go in the I position

So that's 10*10*10*10*10*10*10*10*10 = 1000000000.

Edwin