# 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

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 Question 405166: 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 number may begin with 0). The answer is supposed to be 1/10^8 Thanks.Answer by Edwin McCravy(8879)   (Show Source): You can put this solution on YOUR website!```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```