document.write( "Question 1055924: If the letters word'DAUGHTER'are to be arranged so that vowels occupy the odd places, then the number
\n" ); document.write( "of different words are? (Solved by only permutations ) \n" ); document.write( "
Algebra.Com's Answer #671175 by Edwin McCravy(20055)\"\" \"About 
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document.write( "D A U G H T E R\r\n" );
document.write( "1 2 3 4 5 6 7 8\r\n" );
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document.write( "[Notice that DAUGHTER itself is NOT one of the \r\n" );
document.write( "required permutations because A is in position 2,\r\n" );
document.write( "which is not an odd position]\r\n" );
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document.write( "There are 4 odd positions: 1,3,5,7.\r\n" );
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document.write( "There are 3 vowels: A,E,U\r\n" );
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document.write( "An example of one of the desired permutations would \r\n" );
document.write( "be RTEHAGUD, \r\n" );
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document.write( "R T E H A G U D\r\n" );
document.write( "1 2 3 4 5 6 7 8\r\n" );
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document.write( "Take away the consonants and leave only the\r\n" );
document.write( "vowels for illustration:\r\n" );
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document.write( "    E   A   U  \r\n" );
document.write( "1 2 3 4 5 6 7 8\r\n" );
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document.write( "The permutation of odd positions chosen here\r\n" );
document.write( "for A,E,U were 5,3,7 respectively.\r\n" );
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document.write( "We placed the A in position 5, the E in position 3, \r\n" );
document.write( "and the U in position 5.\r\n" );
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document.write( "    E   A   U  \r\n" );
document.write( "1 2 3 4 5 6 7 8\r\n" );
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document.write( "There are 4P3 permutations of 3 of the odd positions 1,3,5,7\r\n" );
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document.write( "The one that was chosen in this example was 5,3,7.\r\n" );
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document.write( "In that example, We placed A in the odd position 5 that \r\n" );
document.write( "came first in the PERMUTATION 5,3,7 of odd positions,\r\n" );
document.write( "(not that came first in the word!).  \r\n" );
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document.write( "Then we placed E in the odd position that came second \r\n" );
document.write( "in the PERMUTATION 5,3,7 of odd positions, (not that \r\n" );
document.write( "came second in the word!).  \r\n" );
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document.write( "Finally we placed U in the odd position that came \r\n" );
document.write( "third in the PERMUTATION 5,3,7 of odd positions, (not that \r\n" );
document.write( "came third in the word!)\r\n" );
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document.write( "There are 5 remaining positions in which to place the 5 \r\n" );
document.write( "remaining letters which is 5P5.\r\n" );
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document.write( "Answer: (4P3)(5P5) = 24(120) = 2880.\r\n" );
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document.write( "Edwin
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