document.write( "Question 405166: A typical social security number is 413-22-9802. If a social security number is chosen at random, what is the probability that all the digits will be the same? (social security number may begin with 0).\r
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Algebra.Com's Answer #286238 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "There are only 10 such social security numbers:\r\n" );
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document.write( " 1. 000-00-0000\r\n" );
document.write( " 2. 111-11-1111\r\n" );
document.write( " 3. 222-22-2222\r\n" );
document.write( " 4. 333-33-3333\r\n" );
document.write( " 5. 444-44-4444\r\n" );
document.write( " 6. 555-55-5555\r\n" );
document.write( " 7. 666-66-6666\r\n" );
document.write( " 8. 777-77-7777\r\n" );
document.write( " 9. 888-88-8888\r\n" );
document.write( "10. 999-99-9999\r\n" );
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document.write( "There are one billion possible social security numbers.  There are\r\n" );
document.write( "two ways to get that.  Either making a list and realizing that\r\n" );
document.write( "a list would be like this:\r\n" );
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document.write( "         1. 000-00-0000\r\n" );
document.write( "         2. 000-00-0001\r\n" );
document.write( "         3. 000-00-0002\r\n" );
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document.write( "         ..............\r\n" );
document.write( "         ..............\r\n" );
document.write( "         ..............\r\n" );
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document.write( " 999999998. 999-99-9997\r\n" );
document.write( " 999999999. 999-99-9998\r\n" );
document.write( "1000000000. 999-99-9999 \r\n" );
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document.write( "or by saying:\r\n" );
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document.write( "There are 10 way to choose the 1st digit.\r\n" );
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document.write( "For each of the 10 or 101\r\n" );
document.write( "ways to choose the first digit, there are 10 ways to choose the \r\n" );
document.write( "2nd digit, so there are 10×10 or 100 or\r\n" );
document.write( "102 ways to choose the first 2 digits.\r\n" );
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document.write( "For each of the 10×10 or 100 or 102\r\n" );
document.write( "ways to choose the first 2 digits, there are 10 ways to choose the \r\n" );
document.write( "3rd digit, so there are 10×10×10 or 1000 or\r\n" );
document.write( "103 ways to choose the first 3 digits.\r\n" );
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document.write( "For each of the 10×10×10 or 1000 or 103\r\n" );
document.write( "ways to choose the first 3 digits, there are 10 ways to choose the \r\n" );
document.write( "4th digit, so there are 10×10×10×10 or 10000 or\r\n" );
document.write( "104 ways to choose the first 4 digits.\r\n" );
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document.write( "For each of the 10×10×10×10 or 10000 or 104\r\n" );
document.write( "ways to choose the first 4 digits, there are 10 ways to choose the \r\n" );
document.write( "5th digit, so there are 10×10×10×10×10 or 100000 or\r\n" );
document.write( "105 ways to choose the first 5 digits.\r\n" );
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document.write( "For each of the 10×10×10×10×10 or 100000 or 105\r\n" );
document.write( "ways to choose the first 5 digits, there are 10 ways to choose the \r\n" );
document.write( "6th digit, so there are 10×10×10×10×10×10 or 1000000 or\r\n" );
document.write( "106 ways to choose the first 6 digits.\r\n" );
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document.write( "For each of the 10×10×10×10×10×10 or 1000000 or 106\r\n" );
document.write( "ways to choose the first 6 digits, there are 10 ways to choose the \r\n" );
document.write( "7th digit, so there are 10×10×10×10×10×10×10 or 10000000 or\r\n" );
document.write( "107 ways to choose the first 7 digits.\r\n" );
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document.write( "For each of the 10×10×10×10×10×10×10 or 10000000 or 107\r\n" );
document.write( "ways to choose the first 7 digits, there are 10 ways to choose the \r\n" );
document.write( "8th digit, so there are 10×10×10×10×10×10×10×10 or 100000000 or\r\n" );
document.write( "108 ways to choose the first 8 digits.\r\n" );
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document.write( "For each of the 10×10×10×10×10×10×10×10 or 100000000 or 108\r\n" );
document.write( "ways to choose the first 8 digits, there are 10 ways to choose the \r\n" );
document.write( "9th digit, so there are 10×10×10×10×10×10×10×10×10 or 1000000000 or\r\n" );
document.write( "109 ways to choose the first 9 digits.\r\n" );
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document.write( "So the probability is 10 ways out of a billion, or\r\n" );
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document.write( "    \"10%2F1000000000=+10%5E1%2F10%5E9+=+1%2F10%5E8\"\r\n" );
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document.write( "Edwin
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