document.write( "Question 849374: Joey prepares 3 cards for his 3 girlfriends. He addresses 3 corresponding envelopes. A brown-out suddenly occurred and he hurriedly placed the cards in the envelope at random. What is the probability that
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Algebra.Com's Answer #511502 by Edwin McCravy(20060)\"\" \"About 
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Joey prepares 3 cards for his 3 girlfriends. He addresses 3 corresponding
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document.write( "1 way out of 3! or 1/3! or 1/6\r\n" );
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\n" ); document.write( "b. No card is sent to the proper addressee?
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document.write( "That's 1 out of 3 sub-factorial.  But if you haven't studied sub-factorials,\r\n" );
document.write( "then we have to list the ways they could have all gone wrong. Girlfriend 1\r\n" );
document.write( "could have been sent card 2 or 3, and in either case there is only one\r\n" );
document.write( "way the other one could have gone wrong.\r\n" );
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document.write( "gf       1  2  3\r\n" );
document.write( "card     2  3  1\r\n" );
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document.write( "or\r\n" );
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document.write( "gf       1  2  3\r\n" );
document.write( "card     3  1  2\r\n" );
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document.write( "[Actually 3 sub-factorial = 3!(1/0!-1/1!+1/2!-1/3!) = 6(1/1-1/1+1/2-1/6) =\r\n" );
document.write( "6(1/2-1/6) = 6(3/6-1/6) = 6(2/6) = 2]\r\n" );
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document.write( "So there are only 2 ways the cards could have all gone wrong: \r\n" );
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document.write( "2/3! = 2/6 = 1/3\r\n" );
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document.write( "Edwin
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