document.write( "Question 112636: A. How many 10-digit phone numbers in the 972 area code have at least one repeated digit?
\n" ); document.write( "B. How many 7-digit phone numbers in the 972 area code have at least one 1 and at least one 3 among its digits?
\n" ); document.write( "Note: 0 or 1 can not be used as the first digit. \n" ); document.write( "
Algebra.Com's Answer #82142 by Edwin McCravy(20056)\"\" \"About 
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document.write( "A. How many 10-digit phone numbers in the 972 area code have at\r\n" );
document.write( " least one repeated digit? \r\n" );
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document.write( "Note: 0 or 1 can not be used as the first digit.\r\n" );
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document.write( "The note should have explained that what it means by the \"first\r\n" );
document.write( "digit\" is really the FOURTH digit when the area code is included.\r\n" );
document.write( "As you know, u8sually within an area code you do not dial the area\r\n" );
document.write( "code, so to dial, say, 972-855-0211, you only have to dial 855-0211,\r\n" );
document.write( "so the FIRST digit you dial is 8, not 9. \r\n" );
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document.write( "Strategy:\r\n" );
document.write( "I.   Calculate the number of phone numbers possible in the 972 area \r\n" );
document.write( "whether with repeated digits or not.\r\n" );
document.write( "II.  Calculate the number of phone numbers with no repeated digits.\r\n" );
document.write( "III. Subtract the results of II from the results of I.\r\n" );
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document.write( "I.  Calculate the number of phone numbers possible in the 972 area \r\n" );
document.write( "whether with repeated digits or not.\r\n" );
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document.write( "Such a number might be 972-312-5925\r\n" );
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document.write( "We can choose a digit where the first 9 is only 1 way, a 9.\r\n" );
document.write( "We can choose a digit where the 7 is only 1 way, a 7.\r\n" );
document.write( "We can choose a digit where the first 2 is only 1 way, a 2.\r\n" );
document.write( "We can choose a digit where the 3 is any of 5 ways.\r\n" );
document.write( "(This is because the 3 is the \"real\" FIRST digit and we can't \r\n" );
document.write( " choose 9 or 7 or 2 or 0 or 1 for it, leaving only 5 digits.)\r\n" );
document.write( "We can choose a digit where the 1 is any of 10 ways.\r\n" );
document.write( "We can choose a digit where the second 2 is any of 10 ways.\r\n" );
document.write( "We can choose a digit where the first 5 is any of 10 ways.\r\n" );
document.write( "We can choose a digit where the second 9 is any of 10 ways.\r\n" );
document.write( "We can choose a digit where the third 2 is any of 10 ways.\r\n" );
document.write( "We can choose a digit where the second 5 is any of 10 ways.\r\n" );
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document.write( "So if we multiply those those together we get \r\n" );
document.write( "1×1×1×5×10×10×10×10×10×10 or 5×106 or 5,000,000 \r\n" );
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document.write( "II.  Calculate the number of phone numbers with no repeated digits.\r\n" );
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document.write( "Such a number might be 972-431-8056\r\n" );
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document.write( "We can choose a digit where the 9 is only 1 way, a 9.\r\n" );
document.write( "We can choose a digit where the 7 is only 1 way, a 7.\r\n" );
document.write( "We can choose a digit where the 2 is only 1 way, a 2.\r\n" );
document.write( "We can choose a digit where the 4 is any of 5 ways. \r\n" );
document.write( "(This is because we cannot choose a 1 or 0 since 4 is considered to\r\n" );
document.write( "be the FIRST digit, since we don't call the first digit in the area\r\n" );
document.write( "code the FIRST digit of the number. \r\n" );
document.write( "We can choose a digit where the 3 is any of 6 ways.\r\n" );
document.write( "We can choose a digit where the 1 is any of 5 ways.\r\n" );
document.write( "We can choose a digit where the 8 is any of 4 ways.\r\n" );
document.write( "We can choose a digit where the 0 is any of 3 ways.\r\n" );
document.write( "We can choose a digit where the 5 is any of 2 ways.\r\n" );
document.write( "We can choose a digit where the 6 is only 1 way.\r\n" );
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document.write( "So if we multiply those those together we get 1×1×1×5×6×5×4×3×2×1\r\n" );
document.write( "or 5×6! or 3600   \r\n" );
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document.write( "III. Subtract the results of II from the results of I.\r\n" );
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document.write( "5×106 - 5×6! or 5,000,000 - 3600 or 4,996,400\r\n" );
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document.write( "That's the answer to the first part.  I'll come back later\r\n" );
document.write( "and do the second one.\r\n" );
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document.write( "Edwin
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