document.write( "Question 548357: How many arrangements can be formed of the letters EXAMINATION so that vowels occupy odd places. \n" ); document.write( "

Algebra.Com's Answer #356942 by Edwin McCravy(20055) $\"\"$ $\"About$

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How many arrangements can be formed of the letters EXAMINATION so that vowels occupy odd places.
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document.write( "Look at an arbitrary arrangement with vowels in the odd\r\n" );
document.write( "positions, say, this one:\r\n" );
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document.write( "AMANENITIXO \r\n" );
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document.write( "is composed of the two arrangements\r\n" );
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document.write( "A A E I I O  \r\n" );
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document.write( "   and\r\n" );
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document.write( " M N N T X\r\n" );
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document.write( "The number of distinguishable arrangements of A A E I I O is \r\n" );
document.write( "We have to divide by the factorial of each number of indistinguishable\r\n" );
document.write( "letters. We divided by 2! because of the 2 A's and again by 2! because of\r\n" );
document.write( "the 2 I's.\r\n" );
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document.write( "For each of those, the number of distinguishable arrangements of M N N T X is\r\n" );
document.write( "  We have to divide by the factorial of the number of\r\n" );
document.write( "indistinguishable letters N. So we divided by 2! because of the 2 N's.\r\n" );
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document.write( "So the total number is  \r\n" );
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document.write( "× = 10800\r\n" );
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document.write( "Edwin

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