SOLUTION: A typical social security number is 413-22-9802. If a social security number is chosen at random, what is the probability that all the digits will be the same? (social security num

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 101
ways to choose the first digit, there are 10 ways to choose the 
2nd digit, so there are 10×10 or 100 or
102 ways to choose the first 2 digits.

For each of the 10×10 or 100 or 102
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
103 ways to choose the first 3 digits.

For each of the 10×10×10 or 1000 or 103
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
104 ways to choose the first 4 digits.

For each of the 10×10×10×10 or 10000 or 104
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
105 ways to choose the first 5 digits.

For each of the 10×10×10×10×10 or 100000 or 105
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
106 ways to choose the first 6 digits.

For each of the 10×10×10×10×10×10 or 1000000 or 106
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
107 ways to choose the first 7 digits.

For each of the 10×10×10×10×10×10×10 or 10000000 or 107
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
108 ways to choose the first 8 digits.

For each of the 10×10×10×10×10×10×10×10 or 100000000 or 108
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
109 ways to choose the first 9 digits.


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

    

Edwin