document.write( "Question 875373: How many distinct arrangements can be made with the letters in the word CINCINNATI \n" ); document.write( "
Algebra.Com's Answer #528380 by Edwin McCravy(20056)\"\" \"About 
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document.write( "If the like letters of CINCINNATI were subscripted differently, \r\n" );
document.write( "like this:\r\n" );
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document.write( "C1I1N1C2I2N2N3ATI3\r\n" );
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document.write( "There would be 10! distinguishable permutations.\r\n" );
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document.write( "If we take the subscripts off the C's, there will be 2! \r\n" );
document.write( "exact duplicates among the 10!\r\n" );
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document.write( "So we must divide the 10! by 2! and get \"10%21%2F2%21\" distinguishable\r\n" );
document.write( "permutations of\r\n" );
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document.write( "CI1N1CI2N2N3ATI3 \r\n" );
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document.write( "If we take the subscripts off the I's, there will be 3! \r\n" );
document.write( "exact duplicates among the \"10%21%2F2%21\"\r\n" );
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document.write( "So we must divide the \"10%21%2F2%21\" by 3! and get \"10%21%2F%282%213%21%29\" \r\n" );
document.write( "distinguishable permutations of\r\n" );
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document.write( "CIN1CIN2N3ATI\r\n" );
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document.write( "If we take the subscripts off the N's, there will be 3! \r\n" );
document.write( "exact duplicates among the \"10%21%2F%282%213%21%29\"\r\n" );
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document.write( "So we must divide the \"10%21%2F%282%213%21%29\" by 3! and get \"10%21%2F%282%213%213%21%29\" \r\n" );
document.write( "distinguishable permutations of\r\n" );
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document.write( "CINCINNATI\r\n" );
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document.write( "Answer: \"10%21%2F%282%213%213%21%29\" = \"3628800%2F%282%2A6%2A6%29\" = \"3628800%2F72\" = 50400.\r\n" );
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document.write( "Edwin
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