document.write( "Question 892342: In a train compartment, there are 8 seats, with 4 facing the front and 4 facing backwards. Find the probability that 2 particular people will sit opposite each other if seating is arranged at random. \n" ); document.write( "

Algebra.Com's Answer #540475 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "Suppose the 8 seats are labeled \r\n" );
document.write( "\r\n" );
document.write( "A,B,C,D,E,F,G,H \r\n" );
document.write( "\r\n" );
document.write( "with\r\n" );
document.write( "\r\n" );
document.write( "1.  seat A opposite seat E,\r\n" );
document.write( "2.  seat B opposite seat F,\r\n" );
document.write( "3.  seat C opposite seat G,\r\n" );
document.write( "4.  seat D opposite seat H\r\n" );
document.write( "\r\n" );
document.write( "The two people can choose a pair of seats in any of C(8,2) = 28 ways.\r\n" );
document.write( "They can choose a pair of opposite seats in only 4 ways.\r\n" );
document.write( "\r\n" );
document.write( "So the probability is 4 out of 28 ways or  which reduces to .\r\n" );
document.write( "\r\n" );
document.write( "--------------------------\r\n" );
document.write( "Explanation:\r\n" );
document.write( "\r\n" );
document.write( "That's these four choices of ways to sit opposite each other:  \r\n" );
document.write( "\r\n" );
document.write( "{A,E} {B,F} (C,G}, {D,H}\r\n" );
document.write( "\r\n" );
document.write( "out of these 28 ways to sit opposite or not:\r\n" );
document.write( "\r\n" );
document.write( "{A,B), {A,C}, {A,D}, {A,E}, {A,F}, {A,G}, {A,H}\r\n" );
document.write( "{B,C), {B,D}, {B,E}, {B,F}, {B,G}, {B,H}, {C,D}\r\n" );
document.write( "{C,E), {C,F}, {C,G}, {C,H}, {D,E}, {D,F}, {D,G}\r\n" );
document.write( "{D,H), {E,F}, {E,G}, {E,H}, {F,G}, {F,H}, {G,H}\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );