document.write( "Question 375018: How many 10 digit numbers can be formed if the first three digits are 407? \n" ); document.write( "

Algebra.Com's Answer #266721 by Edwin McCravy(20056) $\"\"$ $\"About$

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How many 10 digit numbers can be formed if the first three digits are 407
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document.write( "There are two methods.  I'll do both.\r\n" );
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document.write( "The largest 10 digit number that has the first three digits 407 is\r\n" );
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document.write( "4079999999\r\n" );
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document.write( "and that number is the the number of positive integers from 1 to 4079999999,\r\n" );
document.write( "inclusively.\r\n" );
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document.write( "We wish to subtract from that the number of integers less than that number\r\n" );
document.write( "which do not have 407 as its first three digits.\r\n" );
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document.write( "The largest 10-digit number that does not have its first three digits as 407 is\r\n" );
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document.write( "4069999999\r\n" );
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document.write( "and that is the number of positive integers from 1 to 4069999999, inclusively.\r\n" );
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document.write( "So we subtract the second number from the first number:\r\n" );
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document.write( " 4079999999\r\n" );
document.write( "-4069999999\r\n" );
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document.write( "   10000000\r\n" );
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document.write( "Or we could do it as an arithmetic sequence:\r\n" );
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document.write( "Then use the formula\r\n" );
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document.write( "Edwin

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