document.write( "Question 1207172: April, Bill , Candace, and Bobby are to be seated at random in a row of
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Algebra.Com's Answer #844902 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "April, Bill , Candace, and Bobby are to be seated at random in a row of
\n" ); document.write( "8 chairs. What is the probability that April and Bobby will occupy
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document.write( "April   can occupy any of 8 seats;\r\n" );
document.write( "Bill    can occupy any of 7 remaining seats;\r\n" );
document.write( "Candace can occupy any of 6 remaining seats;\r\n" );
document.write( "Bobby   can occupy any of 5 remaining seats.\r\n" );
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document.write( "In all, there are 8*7*6*5 = 1680 possible different placements.\r\n" );
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document.write( "The favorable placements are \r\n" );
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document.write( "    (a)  April is at the most left seat; Bobby is at the most right seat;\r\n" );
document.write( "         two other persons in any 2 of 6 remaining seats,\r\n" );
document.write( "         which gives 6*5 = 30 options.\r\n" );
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document.write( "    (b)  April is at the most right seat; Bobby is at the most left seat;\r\n" );
document.write( "         two other persons in any 2 of 6 remaining seats,\r\n" );
document.write( "         which gives 6*5 = 30 other options.\r\n" );
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document.write( "Therefore, the desired probability is  P =  =  = .\r\n" );
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document.write( "ANSWER.  The desired probability is 1/28.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The problem's formulation is not totally clear and admits different interpretations.\r
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\n" ); document.write( "\n" ); document.write( "My interpretation was that April and Bobby occupy the seats at two opposite ends of the row.\r
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\n" ); document.write( "\n" ); document.write( "Other possible interpretation can be that April and Bobby occupy two adjacent seats at some of the two ends.\r
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\n" ); document.write( "\n" ); document.write( "When a problem admits different interpretations, it is a fault of its creator.\r
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