document.write( "Question 740459: How many permutations of the digits 0, 1, 2, . . . , 9 either
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Algebra.Com's Answer #852587 by ikleyn(53418) $\"\"$ $\"About$

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document.write( "Let P be the set of permutations of the digits 0, 1, 2, . . . , 9 that start with a 3. \r\n" );
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document.write( "This set has 9! permutations.\r\n" );
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document.write( "Let Q be the set of permutations of the digits 0, 1, 2, . . . , 9 that end with a 7. \r\n" );
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document.write( "This set has 9! permutations.\r\n" );
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document.write( "The sets P and Q have non-empty intersection set: it consist of all permutations that\r\n" );
document.write( "start with a 3 and end with a 7.\r\n" );
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document.write( "This set (P ∩ Q) has 8! permutations.\r\n" );
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document.write( "So, the answer to the problem's question is this number\r\n" );
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document.write( "    9! + 9! - 8! = 2*1*2*3*4*5*6*7*8*9 - 1*2*3*4*5*6*7*8 = 685440.\r\n" );
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