document.write( "Question 472787: The letters of DIRECTOR are arranged at random. What is the probability of vowels occupying ONLY even places.
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Algebra.Com's Answer #324138 by Edwin McCravy(20055) $\"\"$ $\"About$

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The letters of DIRECTOR are arranged at random. What is the probability of vowels occupying ONLY even places.
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document.write( "DIRECTOR has 5 consonants (C) and 3 vowels (V).  There are 4 even places \r\n" );
document.write( "but only 3 vowels.  So we choose 3 of the 4 even places to put the 3\r\n" );
document.write( "vowels.  So we can chose 3 of the 4 even places to  \r\n" );
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document.write( "So it has one of these C(4,3) forms:\r\n" );
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document.write( "CVCVCVCC, CVCVCCCV, CVCCCVCV, or CCCVCVCV\r\n" );
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document.write( "Every one of these C(4,3) ways to place the 3 vowels leaves the \r\n" );
document.write( "remaining 5 consonants D,R,C,T,R\r\n" );
document.write( "to arrange around them.  The 2 R's are indistinguishable, so for each \r\n" );
document.write( "of the C(4,1) ways there are  ways to rearrange D,R,C,T,R\r\n" );
document.write( "around the three vowels. So the numerator of the probabiliy is:\r\n" );
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document.write( "C(4,3)* = 240\r\n" );
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document.write( "The denominator is the number of ways to arrange the letters DIRECTOR\r\n" );
document.write( "in any manner, with the 2 R's indistinguishable:\r\n" );
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document.write( " = 20160\r\n" );
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document.write( "So the desired probability is  = 1/84\r\n" );
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document.write( "Edwin

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