document.write( "Question 1194073: if the letters A, B, C, D, E and F are randomly arranged, calculate the probability that the letters A and B will be next to each other? \r
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Algebra.Com's Answer #826172 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "if the letters A, B, C, D, E and F are randomly arranged, calculate the probability
\n" ); document.write( "that the letters A and B will be next to each other?
\n" ); document.write( "Textbook answer is 1/3.
\n" ); document.write( "Can someone help me solve this problem? Thanks.
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document.write( "In all, there are 6 letters, A, B, C, D, E and F.   The numbers of all possible permutations is 6!.\r\n" );
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document.write( "IF the letters A and B form one block AB, then we have, actually, 5 objects to permute: \r\n" );
document.write( "4 letters C, D, E anf F plus one block AB.\r\n" );
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document.write( "5 objects can be arranged in 5! different ways.\r\n" );
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document.write( "If the letters A and B form one block  BA   (in this order !),  then another 5! different favorable permutations possible.\r\n" );
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document.write( "Thus the number of all favorable permutations with A and B next to each other is 2*5!.\r\n" );
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document.write( "Now the sought probability is the ratio of these two numbers\r\n" );
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document.write( "    P =  =  = .    ANSWER\r\n" );
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