Social Security Numbers - Math Central

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How many different number combinations are there for the social security system? We know that there are only a certain ammount of combinations available and the current US population is at 281 million. The number system should include as many nine digit combinations as possible using the numbers 0-9 in multiple different spots. Thank you for all of your help. I need to win this bet! Sincerely yours Chris
Hi Chris, A social security number is a 9 digit number and if all combinations of 9 digits were valid social security numbers the number possible would be 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 1 000 000 000 It's relatively easy to see why this is true. For a one digit number you have 10 possibilities, 0,1,2,3,4,5,6,7,8 and 9. If you add a second digit you have ten times as many possibilities, 10 that start with zero, 00,01,02...,09; ten that start with one, 10,11,12,...,19 and so on. Thus 10 x 10 possible 2 digit numbers. If you add a third digit you have ten times as many as the number of two digit numbers, that is 10 x 10 x 10. Continuing this for 9 digits gives the number above. Unfortunately the system is not that simple. There are some 9 digit numbers that are not "valid" social security numbers. I suggest that you look at http://www.searchbug.com/peoplefinder/ssn-invalid.aspx Penny
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