document.write( "Question 1025274: What is distinguishable permutations
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Algebra.Com's Answer #640550 by Edwin McCravy(20060) $\"\"$ $\"About$
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document.write( "Take the word DEED\r\n" );
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document.write( "If we make one D capital and the other small d and\r\n" );
document.write( "do the same with the E, we have these \r\n" );
document.write( "4! = 4*3*2*1 = 4P4 = 24 permutations:\r\n" );
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document.write( "1.  DdEe\r\n" );
document.write( "2.  DdeE\r\n" );
document.write( "3.  DEde\r\n" );
document.write( "4.  DEed\r\n" );
document.write( "5.  DedE\r\n" );
document.write( "6.  DeEd\r\n" );
document.write( "7.  dDEe\r\n" );
document.write( "8.  dDeE\r\n" );
document.write( "9.  dEDe\r\n" );
document.write( "10.  dEeD\r\n" );
document.write( "11.  deDE\r\n" );
document.write( "12.  deED\r\n" );
document.write( "13.  EDde\r\n" );
document.write( "14.  EDed\r\n" );
document.write( "15.  EdDe\r\n" );
document.write( "16.  EdeD\r\n" );
document.write( "17.  EeDd\r\n" );
document.write( "18.  EedD\r\n" );
document.write( "19.  eDdE\r\n" );
document.write( "20.  eDEd\r\n" );
document.write( "21.  edDE\r\n" );
document.write( "22.  edED\r\n" );
document.write( "23.  eEDd\r\n" );
document.write( "24.  eEdD\r\n" );
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document.write( "For instance, we can tell the difference between \r\n" );
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document.write( "EDed, EdeD, eDEd, and edED\r\n" );
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document.write( "But if we spell them all with capital letters we cannot\r\n" );
document.write( "tell them apart.  They all look like EDED.  So we cannot\r\n" );
document.write( "distinguish them, so we label them \"indistinguishable\".\r\n" );
document.write( "However we can tell the difference between EDED and DEDE.\r\n" );
document.write( "They are \"distinguishable\".\r\n" );
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document.write( "So there are only 6 distinguishable permutations of DEED.\r\n" );
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document.write( "They are\r\n" );
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document.write( "1. DDEE\r\n" );
document.write( "2. DEDE\r\n" );
document.write( "3. DEED\r\n" );
document.write( "4. EDDE\r\n" );
document.write( "5. EDED\r\n" );
document.write( "6. EEDD\r\n" );
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document.write( "That's because the 4! = 4*3*2*1 4P4 = 24 counts each one\r\n" );
document.write( "2! = 2*1 = 2P2 = 2 times too many for the D's and also\r\n" );
document.write( "2 times too many for the E's.  Tham means that the 24\r\n" );
document.write( "counts each permutation 4 times too many.  So to get the \r\n" );
document.write( "6, we begin with the 24! and divide by the product of each \r\n" );
document.write( "of the factorials of the numbers of indistinguishable letters.\r\n" );
document.write( "So we divide 24 by 2! and again by 2! so we end up dividing\r\n" );
document.write( "24 by 4 getting 6.\r\n" );
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document.write( " =  =  = \r\n" );
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document.write( "The number of distinguishable permutations of the word PEPPER\r\n" );
document.write( "is  =  =  = \r\n" );
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document.write( "We divide 6! by 3! for the indistinguishable P's and by 2!\r\n" );
document.write( "for the indistinguishable E's.\r\n" );
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document.write( "The number of distinguishable permutations of the word MISSISSIPPI\r\n" );
document.write( "is  = \r\n" );
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document.write( "We divide 11! by 4! for the indistinguishable I's, by 4! for the\r\n" );
document.write( "for the indistinguishable S's, and by 2! for the indistinguishable\r\n" );
document.write( "P's.\r\n" );
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document.write( "Edwin
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