document.write( "Question 541020: distinguish permutation of the word decreed \n" ); document.write( "

Algebra.Com's Answer #353989 by AnlytcPhil(1806) $\"\"$ $\"About$

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document.write( "If we could tell the two d's apart, and the three e's apart, and the\r\n" );
document.write( "word were written like this:\r\n" );
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document.write( "decrEᕮD\r\n" );
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document.write( "then the answer would be 7! = 5040\r\n" );
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document.write( "However if we take a random permutation of that, say\r\n" );
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document.write( "cᕮDerdE\r\n" );
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document.write( "There are 3! ways to arrange the ᕮ, e, and E within that permutation,\r\n" );
document.write( "and every other permutation of decrEᕮD is the same way, so that\r\n" );
document.write( "means that the 7! or 5040 counts the same permutation 3! of 6 times too\r\n" );
document.write( "many, so we must divide by 3! or 6.\r\n" );
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document.write( "But there are also 2! ways the D and d can be arranged, so we must\r\n" );
document.write( "also divide by 2!, since we cannot tell the D from the d when they are\r\n" );
document.write( "both small d's.  Therefore the number of distinguishable ways when\r\n" );
document.write( "all the e's look alike and both the d's look alike, is given by\r\n" );
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document.write( " =  =  = 420    \r\n" );
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document.write( "Edwin

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