document.write( "Question 1177980: A car is parked among N cars in a row, not at either end. On this return the owner finds that exactly r
\n" ); document.write( "of the N places are still occupied. What is the probability that both neighbouring places are empty. \n" ); document.write( "
Algebra.Com's Answer #850425 by ikleyn(53763)\"\" \"About 
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\n" ); document.write( "A car is parked among N cars in a row, not at either end. On this return the owner finds that exactly r
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\n" ); document.write( "\n" ); document.write( "My solution here is another way to organize your thoughts and to present a solution.\r
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\n" ); document.write( "\n" ); document.write( "For clarity, I will re-formulate the problem in this way.\r
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document.write( "    In a parking lot, there are N parking places, in a row.\r\n" );
document.write( "    Originally, they all are occupied by cars.\r\n" );
document.write( "    The owner's car is parked among these N cars, not at either end.\r\n" );
document.write( "    On his return the owner finds that exactly r of the N places are still occupied.\r\n" );
document.write( "    What is the probability that both neighboring places are empty ?\r\n" );
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\n" ); document.write( "\n" ); document.write( "Below is the solution for this modified formulation.\r
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document.write( "There are N places in a row at the table.\r\n" );
document.write( "One place is marked \"C\" (symbolizing your car), which is not at either end.\r\n" );
document.write( "You have (N-r) cards in your hands with letter E (symbolizing \"empty place\").\r\n" );
document.write( "You distribute these r cards randomly over all the unmarked places.\r\n" );
document.write( "What is the probability that two neighboring places to \"C\" will be \"E\".\r\n" );
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document.write( "The probability that the left place is card \"E\" is  \"%28N-r%29%2F%28N-1%29\".\r\n" );
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document.write( "The probability that the right place is card \"E\" is then  \"%28N-r-1%29%2F%28N-2%29\".\r\n" );
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document.write( "The overall probability that both neighbouting cards are \"E\", is the product  \r\n" );
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document.write( "    P = \"%28%28N-r%29%2F%28N-1%29%29%2A%28%28N-r-1%29%2F%28N-2%29%29\".    ANSWER\r\n" );
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