document.write( "Question 872973: Find the number of distinguishable permutations of the letters int he words Alabama,algebra and florida \n" ); document.write( "

Algebra.Com's Answer #526616 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "If \"ALABAMA\" were written so that the A's were of different colors,\r\n" );
document.write( "like this, \"ALABAMA\", the number of permutations would be 7!.  However,\r\n" );
document.write( "since the four A's look exactly alike in \"ALABAMA\", the number of\r\n" );
document.write( "distinguishable permutations is much smaller.  So what we do is start \r\n" );
document.write( "with the 7! arrangements of \"ALABAMA\", and divide by the number of ways\r\n" );
document.write( "the four A's can be arranged within each permutation, so that in effect\r\n" );
document.write( "they will all be counted only once.\r\n" );
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document.write( "So the answer is  =  = 210. \r\n" );
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document.write( "\"ALGEBRA\" has  =  = 2520 distinguishable permutations, we only need \r\n" );
document.write( "to divide by 2 because there are only 2 A's that are indistinguishable.\r\n" );
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document.write( "FLORIDA has 7! = 5040 distinguishable permutations.  We don't need to \r\n" );
document.write( "divide by anything because all 7 letters are distinguishable.  \r\n" );
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document.write( "Edwin

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