document.write( "Question 1206447: Six story books, A, B, C, D, E, and F were arranged on a shelf randomly. If A and B were not placed together, what is the probability that there was one book between A and B? \n" ); document.write( "
Algebra.Com's Answer #843947 by Edwin McCravy(20055)\"\" \"About 
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document.write( "Consider putting A in one on those first 4 spaces and\r\n" );
document.write( "B somewhere to the right of it.\r\n" );
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document.write( "_C_D_E_F_ \r\n" );
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document.write( "Successful ways:\r\n" );
document.write( "We can pick a letter to put A immediately before and B immediately after\r\n" );
document.write( "in 4 ways.\r\n" );
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document.write( "_C_D_E_F_\r\n" );
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document.write( "Possible ways:\r\n" );
document.write( "We can choose a pair of spaces from the 5 to put A in the leftmost one \r\n" );
document.write( "and B in the rightmost one in C(5,2) = 10 ways.\r\n" );
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document.write( "The probability is 4/10 or 2/5.  The ratio is the same for any arrangement\r\n" );
document.write( "of CDEF, and either arrangement of AB, so that's the final answer. \r\n" );
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document.write( "[If we like we could multiply numerator and denominator by the 4! ways to\r\n" );
document.write( "arrange CDEF and also by 2! for the 2 arrangements of AB, but why bother?\r\n" );
document.write( "The ratio, i.e., the probability, would be the same.]\r\n" );
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document.write( "Edwin
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