document.write( "Question 1051106: How many different permutations of the letters in the word CINCINNATI are there? \n" ); document.write( "

Algebra.Com's Answer #666700 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "How many different permutations of the letters in the word CINCINNATI are there?
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document.write( " = 50400.\r\n" );
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document.write( "In all, there are 10 letters in the word.\r\n" );
document.write( "Of them, C is repeated 2 times, I is repeated 3 times, and N is repeated 3 times.\r\n" );
document.write( "The rest of the letters are unique.\r\n" );
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document.write( "The factors in the denominator, from left to right, are:\r\n" );
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document.write( "2! in the denominator is for C which is repeated 2 times in the word;\r\n" );
document.write( "3! in the denominator is for I which is repeated 3 times in the word;\r\n" );
document.write( "3! in the denominator is for N which is repeated 3 times in the word.\r\n" );
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