document.write( "Question 1191629: How many distinct permutations of 4 letters from EAGLES are there? (I believe this question uses cases) \n" ); document.write( "

Algebra.Com's Answer #823414 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "How many distinct permutations of 4 letters from EAGLES are there? (I believe this question uses cases)
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\n" ); document.write( "\n" ); document.write( "The word EAGLES has 6 letters; of them, one letter E is repeated and have a multiplicity 2.\r
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\n" ); document.write( "\n" ); document.write( "When we analyze the number of different words of 4 letters formed from the given word (symbols),\r
\n" ); document.write( "\n" ); document.write( "we should distinct two different cases.\r
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document.write( "Case 1.  All 4 letters in the final word are different.\r\n" );
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document.write( "         In this case, we have only 5 distinct letters to choose from, (E, A, G, L S);\r\n" );
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document.write( "         therefore, the number of possible words to form is  5*4*3*2 = 120  in this case  (the order of letters does matter !);\r\n" );
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document.write( "Case 2.  In the final word, we have 2 identical letters E and any 2 of the remaining 4 letters.\r\n" );
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document.write( "         In this case, we can select these two remaining letters by   = 6 different ways,\r\n" );
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document.write( "         and we can arrange then 4 letters with two repeating undistinguishable Es by  \r\n" );
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document.write( "              =  = 12 different distinguishable ways.\r\n" );
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document.write( "         Combining everything altogether, we have 6*12 = 72 different words in Case 2.\r\n" );
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document.write( "Cases (1) and (2) are the disjoint sets of words; therefore, the answer to the problem's question is 120 + 72 = 192.\r\n" );
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document.write( "ANSWER.  192 different / (distinguished) words of the length 4 can be formed.\r\n" );
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