document.write( "Question 981027: How many rearrangements of the letters FACEBOOK have the two O's not together? \n" ); document.write( "

Algebra.Com's Answer #602186 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "How many rearrangements of the letters FACEBOOK have the two O's not together?\r\n" );
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document.write( "First we calculate the number of distinguishable permutations of FACEBOOK\r\n" );
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document.write( "If the O's were distinguishable as FACEBOoK, the number would be 8!\r\n" );
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document.write( "For we would be able to tell the difference between EBKoAFCO and EBKOAFCo.\r\n" );
document.write( "But since we cannot tell the O's apart we must divide by 2!\r\n" );
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document.write( "No of distinguishable arrangements of FACEBOOK  = 20160.\r\n" );
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document.write( "From this number we must subtract the number of ways the O's come together.\r\n" );
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document.write( "Then we have the 7 things {F,A,C,E,B,(OO),K} to arrange and they are all\r\n" );
document.write( "distinguishable.  [Notice that the double O is considered as just one thing.]\r\n" );
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document.write( "So there are 7! ways of arranging those 7 things.\r\n" );
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document.write( "Final answer =  = .\r\n" );
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document.write( "Edwin

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