SOLUTION: Combinatorics: How many social security numbers can a state official have under the following schemes? Which of the two schemes will generate enough social security numbers to cove

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Question 649391: Combinatorics: How many social security numbers can a state official have under the following schemes? Which of the two schemes will generate enough social security numbers to cover a population of 3,800,000 people?
1. A social security number can begin with any number but two even numbers or two odd numbers cannot be next to each other.
2. All numbers can be used anywhere but without repetitions.

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Social security numbers are of the form xxx-xx-xxxx

The first way: 

they can be either of these two forms:

EOE-OE-OEOE or OEO-EO-EOEO

The 5 even digits are 0,2,4,6,8
The 5 odd digits are 1,3,5,7,9

For 5 evens and 4 odds, there are (5·5·5·5·5)(5·5·5·5) = 59 = 1953125
For 5 odds and 4 evens, there are (5·5·5·5·5)(5·5·5·5) = 59 = 1953125

Total  3906250 which is enough for 3800000 

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 The second way:

10·9·8·7·6·5·3·2 = 10! = 3628800, which is not enough for 3800000

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Edwin