document.write( "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?
\n" ); document.write( "1. A social security number can begin with any number but two even numbers or two odd numbers cannot be next to each other.
\n" ); document.write( "2. All numbers can be used anywhere but without repetitions.
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #406935 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Social security numbers are of the form xxx-xx-xxxx\r\n" );
document.write( "\r\n" );
document.write( "The first way: \r\n" );
document.write( "\r\n" );
document.write( "they can be either of these two forms:\r\n" );
document.write( "\r\n" );
document.write( "EOE-OE-OEOE or OEO-EO-EOEO\r\n" );
document.write( "\r\n" );
document.write( "The 5 even digits are 0,2,4,6,8\r\n" );
document.write( "The 5 odd digits are 1,3,5,7,9\r\n" );
document.write( "\r\n" );
document.write( "For 5 evens and 4 odds, there are (5·5·5·5·5)(5·5·5·5) = 59 = 1953125\r\n" );
document.write( "For 5 odds and 4 evens, there are (5·5·5·5·5)(5·5·5·5) = 59 = 1953125\r\n" );
document.write( "\r\n" );
document.write( "Total  3906250 which is enough for 3800000 \r\n" );
document.write( "\r\n" );
document.write( "-------------------\r\n" );
document.write( " The second way:\r\n" );
document.write( "\r\n" );
document.write( "10·9·8·7·6·5·3·2 = 10! = 3628800, which is not enough for 3800000\r\n" );
document.write( "\r\n" );
document.write( "------------------\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );