document.write( "Question 1204716: Find the number of distinguishable permutations of the given letters \"AAABBBCD\".
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Algebra.Com's Answer #841153 by MathLover1(20850) $\"\"$ $\"About$

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permutations of { $\"A\"$ , $\"+A\"$ , $\"A\"$ , $\"B\"$ , $\"B\"$ , $\"+B\"$ , $\"C\"$ , $\"D\"$ }\r
\n" ); document.write( "\n" ); document.write( "there are $\"8\"$ letters
\n" ); document.write( "there are $\"3\"$ $\"A\"$ s and $\"3\"$ $\"B\"$ s, since order matters, there will be following number of permutations :\r
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\n" ); document.write( "\n" ); document.write( " $\"nPr=n%21\"$ /( $\"n%5B1%5D%21\"$ * $\"n%5B2%5D%21\"$ *....* $\"n%5Br%5D%21\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"n=8\"$ \r
\n" ); document.write( "\n" ); document.write( "Distinct subsets:\r
\n" ); document.write( "\n" ); document.write( "Subsets : $\"A+=+3\"$ ; $\"B+=+3\"$ ; $\"C+=+1\"$ ; $\"D+=+1\"$ ;
\n" ); document.write( "Subsets' count: $\"n%5B1%5D%28A%29+=+3\"$ , $\"n%5B2%5D%28B%29+=+3\"$ , $\"n%5B3%5D%28C%29+=+1\"$ , $\"n%5B4%5D%28D%29+=+1\"$ \r
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\n" ); document.write( "\n" ); document.write( "The letters of the word $\"AAABBBCD+\"$ can be arranged in $\"1120\"$ distinct ways.\r
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