document.write( "Question 117046: Find the number of distinguishable permutations of the group of letters: A,A,G,E,E,E,M. \n" ); document.write( "

Algebra.Com's Answer #85117 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "Find the number of distinguishable permutations of the group of letters: $\"A\"$ , $\"A\"$ , $\"G\"$ , $\"E\"$ , $\"E\"$ , $\"E\"$ , $\"M\"$ .\r
\n" ); document.write( "\n" ); document.write( " Here are the frequencies of the letters: $\"A=2\"$ , $\"G=1\"$ , $\"E=3\"$ , $\"M=1\"$ for a total of $\"7\"$ letters.\r
\n" ); document.write( "\n" ); document.write( " $\"n+=+7\"$
\n" ); document.write( "Then the number of distinguishable permutations will be:\r
\n" ); document.write( "\n" ); document.write( " $\"n%21%2F%28%28n1%21%29%28n2%21%29%28n3%21%29%28n4%21%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"7%21%2F%28%282%21%29%281%21%29%283%21%29%281%21%29%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"1%2A2%2A3%2A4%2A5%2A6%2A7%2F%28%281%2A2%29%281%29%281%2A2%2A3%29%281%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"1%2A2%2A3%2A4%2A5%2A6%2A7%2F%282%2A6%29%29\"$ ЕЕЕ do some simplification\r
\n" ); document.write( "\n" ); document.write( " $\"1%2A3%2A4%2A5%2A7\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"420%29\"$
\n" ); document.write( "
\n" ); document.write( "so, the number of distinguishable permutations of the group of letters is $\"420\"$ .
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