document.write( "Question 269159: Sandy typed a positive six-digit integer, but the two 9s she typed didn’t show. If 2010 appeared, how many different positive six-digit integers could she have typed? One such integer to include is 920910. \n" ); document.write( "

Algebra.Com's Answer #197283 by AnlytcPhil(1810) $\"\"$ $\"About$

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Sandy typed a positive six-digit integer, but the two 9s she typed didn’t show. If 2010 appeared, how many different positive six-digit integers could she have typed? One such integer to include is 920910.
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document.write( "There are 5 positions into each of the 9's could have \r\n" );
document.write( "supposed to have been.\r\n" );
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document.write( "1. before the 2\r\n" );
document.write( "2. between the 2 and the 1st 0\r\n" );
document.write( "3. between the 1st 0 and the 1\r\n" );
document.write( "4. between the 1 and the second 0\r\n" );
document.write( "5. after the second 0.\r\n" );
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document.write( "There are two cases:\r\n" );
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document.write( "1. When the two 9's are in different positions \r\n" );
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document.write( "      5C2\r\n" );
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document.write( "2. When both 9's are together in the same position:\r\n" );
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document.write( "      5C1\r\n" );
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document.write( "That's 5C2 + 5C1 = 10 + 5 = 15\r\n" );
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document.write( "Here are the 5C2 or 10 where the 9's are in different\r\n" );
document.write( "positions, not right together:\r\n" );
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document.write( " 1. 929010\r\n" );
document.write( " 2. 920910\r\n" );
document.write( " 3. 920190\r\n" );
document.write( " 4. 920109\r\n" );
document.write( " 5. 290910\r\n" );
document.write( " 6. 290190\r\n" );
document.write( " 7. 290109\r\n" );
document.write( " 8. 209190\r\n" );
document.write( " 9. 209109\r\n" );
document.write( "10. 201909\r\n" );
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document.write( "And here are the 5C1 or the other 5, where the 9's\r\n" );
document.write( "are together in the same position.\r\n" );
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document.write( "11. 992010\r\n" );
document.write( "12. 299010\r\n" );
document.write( "13. 209910\r\n" );
document.write( "14. 201990\r\n" );
document.write( "15. 201099\r\n" );
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document.write( "So there are indeed 15 in all.\r\n" );
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document.write( "Edwin

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