document.write( "Question 1144868: Mary and Tom park their cars in an empty parking lot that consists of N parking spaces in a row,
\n" ); document.write( "where N ≥ 4. Assume that each possible pair of parking locations is equally likely. Calculate the
\n" ); document.write( "probability that the parking spaces they select are exactly 4 apart i.e. exactly three empty spaces between them? \n" ); document.write( "

Algebra.Com's Answer #766053 by ikleyn(52813) $\"\"$ $\"About$

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document.write( "Let's assume that we consider only ORDERED placings.  It means that we consider placings (M,T) and (T,M) as different,\r\n" );
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document.write( "i.e. we account for the order.\r\n" );
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document.write( "Then the total space of possible parking (without imposed constraint) is N*(N-1).\r\n" );
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document.write( "    (they can place their car in any two different positions, but not in one position simultaneously).\r\n" );
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document.write( "The number of possible placings under imposed constrain is 2*(N-3).\r\n" );
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document.write( "The factor 2 accounts for the order (M,T) or (T,M).\r\n" );
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document.write( "Thus the probability under the question is this ratio  .     ANSWER\r\n" );
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\n" ); document.write( "Comment from student : Thank you so much for your time and help!
\n" ); document.write( "But I'm a bit confuse that how total space of possible parking (without imposed constraint) is N*(N-1) ?
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\n" ); document.write( "\n" ); document.write( "My response : Mary can park her car in any of N parking spots.\r
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\n" ); document.write( "\n" ); document.write( "Then Tom can park his car in any of remaining (N-1) parking spots.\r
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\n" ); document.write( "\n" ); document.write( "It gives N*(N-1) possibilities.\r
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document.write( "      By the way, everybody who solves such problem, must know this logic and use it freely in their solutions.\r\n" );
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