document.write( "Question 1198366: How many different 4-letter permutations can be formed from the letters in the word REPRESENT?\r
\n" ); document.write( "\n" ); document.write( "I know that if I want deffrent letter it would be permutation
\n" ); document.write( "like 6P4 = 360\r
\n" ); document.write( "\n" ); document.write( "but how about the repeated letters like the E 3 times and r 2 times? \n" ); document.write( "

Algebra.Com's Answer #831945 by ikleyn(52810) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "How many different 4-letter permutations can be formed from the letters in the word REPRESENT?
\n" ); document.write( "I know that if I want deffrent letter it would be permutation
\n" ); document.write( "like 6P4 = 360
\n" ); document.write( "but how about the repeated letters like the E 3 times and r 2 times?
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document.write( "Since they want you use different letters with no repetition,\r\n" );
document.write( "you should first determine the number of different letters in the word REPRESENT.\r\n" );
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document.write( "It is easy to do: the number of different letters is  R + E + P + S + N + T = 6.\r\n" );
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document.write( "Now you apply the method which you know, and you get this answer:\r\n" );
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document.write( "    the number of different 4-letter permutations is  6*5*4*3 = 360\r\n" );
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document.write( "    (four consecutive integer factors in descending order, starting from the number of 6).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, with complete explanations.\r
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\n" ); document.write( "\n" ); document.write( "        Another interpretation is possible considering/allowing repeating letters.\r
\n" ); document.write( "\n" ); document.write( "        @ewatrr tried to implement it, but her calculations are erroneous.\r
\n" ); document.write( "\n" ); document.write( "        See my calculations for this case below.\r
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document.write( "There are 6 different letters; of them, letter \"E\" has multiplicity 3\r\n" );
document.write( "and letter \"R\" has multiplicity 2.\r\n" );
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document.write( "We have 360 permutations without repetition, as I counted above.\r\n" );
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document.write( "Next, with 3 \"E\" and one single letter from remaining 5 letters {R,P,S,N,T} we have 5*4 = 20 additional permutations.\r\n" );
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document.write( "Next, with 2 \"E\" and 2 \"R\", we have   =  = 6 additional distinguishable permutations.\r\n" );
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document.write( "Next, with 2 \"E\" and 2 other single letters from the remaining 6-1 = 5 other unique letters {R,P,S,N,T}, \r\n" );
document.write( "we have  = 20*6 = 120 additional distinguishable permutations.\r\n" );
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document.write( "Next, with 2 \"R\" and 2 other single letters from the remaining 6-1 = 5 other unique letters {E,P,S,N,T}, \r\n" );
document.write( "we have  = 20*6 = 120 additional distinguishable permutations.\r\n" );
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document.write( "In all, there are  360 + 20 + 6 + 120 + 120 = 626 permutations of this kind.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "So, you have solutions for both possible interpretations.\r
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