Question 405166
<pre>
There are only 10 such social security numbers:

 1. 000-00-0000
 2. 111-11-1111
 3. 222-22-2222
 4. 333-33-3333
 5. 444-44-4444
 6. 555-55-5555
 7. 666-66-6666
 8. 777-77-7777
 9. 888-88-8888
10. 999-99-9999

There are one billion possible social security numbers.  There are
two ways to get that.  Either making a list and realizing that
a list would be like this:

         1. 000-00-0000
         2. 000-00-0001
         3. 000-00-0002

         ..............
         ..............
         ..............

 999999998. 999-99-9997
 999999999. 999-99-9998
1000000000. 999-99-9999 

or by saying:

There are 10 way to choose the 1st digit.

For each of the 10 or 10<sup>1</sup>
ways to choose the first digit, there are 10 ways to choose the 
2nd digit, so there are 10×10 or 100 or
10<sup>2</sup> ways to choose the first 2 digits.

For each of the 10×10 or 100 or 10<sup>2</sup>
ways to choose the first 2 digits, there are 10 ways to choose the 
3rd digit, so there are 10×10×10 or 1000 or
10<sup>3</sup> ways to choose the first 3 digits.

For each of the 10×10×10 or 1000 or 10<sup>3</sup>
ways to choose the first 3 digits, there are 10 ways to choose the 
4th digit, so there are 10×10×10×10 or 10000 or
10<sup>4</sup> ways to choose the first 4 digits.

For each of the 10×10×10×10 or 10000 or 10<sup>4</sup>
ways to choose the first 4 digits, there are 10 ways to choose the 
5th digit, so there are 10×10×10×10×10 or 100000 or
10<sup>5</sup> ways to choose the first 5 digits.

For each of the 10×10×10×10×10 or 100000 or 10<sup>5</sup>
ways to choose the first 5 digits, there are 10 ways to choose the 
6th digit, so there are 10×10×10×10×10×10 or 1000000 or
10<sup>6</sup> ways to choose the first 6 digits.

For each of the 10×10×10×10×10×10 or 1000000 or 10<sup>6</sup>
ways to choose the first 6 digits, there are 10 ways to choose the 
7th digit, so there are 10×10×10×10×10×10×10 or 10000000 or
10<sup>7</sup> ways to choose the first 7 digits.

For each of the 10×10×10×10×10×10×10 or 10000000 or 10<sup>7</sup>
ways to choose the first 7 digits, there are 10 ways to choose the 
8th digit, so there are 10×10×10×10×10×10×10×10 or 100000000 or
10<sup>8</sup> ways to choose the first 8 digits.

For each of the 10×10×10×10×10×10×10×10 or 100000000 or 10<sup>8</sup>
ways to choose the first 8 digits, there are 10 ways to choose the 
9th digit, so there are 10×10×10×10×10×10×10×10×10 or 1000000000 or
10<sup>9</sup> ways to choose the first 9 digits.


So the probability is 10 ways out of a billion, or

    {{{10/1000000000= 10^1/10^9 = 1/10^8}}}

Edwin</pre>