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