document.write( "Question 571843: In how many ways can 5 people be seated on 7 chairs a round table if
\n" ); document.write( "a) only their positions relative to each other count (that is, the arrangements obtained from each other by rotation of all people are considered to be the same)\r
\n" ); document.write( "\n" ); document.write( "b) only who sits next to whom counts, but not on which side (rotations and reflections do not change the arrangement)? \n" ); document.write( "
Algebra.Com's Answer #368230 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
In how many ways can 5 people be seated on 7 chairs a round table if
\n" ); document.write( "a) only their positions relative to each other count (that is, the arrangements obtained from each other by rotation of all people are considered to be the same)
\n" ); document.write( "
\r\n" );
document.write( "First we will calculate the number of ways the 5 could be seated in the 7\r\n" );
document.write( "chairs if the chairs were in a row.\r\n" );
document.write( "\r\n" );
document.write( "Then we will divide by 5 because for every way they could be seated at a round\r\n" );
document.write( "table, there are 5 ways they could sit in the row of chairs that would amount\r\n" );
document.write( "to the same seating arrangement at the round table.\r\n" );
document.write( "\r\n" );
document.write( "So first we work the problem as if the chairs were in a row:\r\n" );
document.write( "\r\n" );
document.write( "If they were in a row. there would be\r\n" );
document.write( "\r\n" );
document.write( "7 places to seat person #1, leaving\r\n" );
document.write( "6 places to seat person #2, leaving\r\n" );
document.write( "5 places to seat person #3, leaving\r\n" );
document.write( "4 places to seat person #4, leaving\r\n" );
document.write( "3 places to seat person #5.\r\n" );
document.write( "\r\n" );
document.write( "That's 7·6·5·4·3 = 2520\r\n" );
document.write( "\r\n" );
document.write( "Then we divide that by 5 rotations and get\r\n" );
document.write( "\r\n" );
document.write( "7·6·4·3 = 504 ways.\r\n" );
document.write( "\r\n" );
document.write( "-------------------------\r\n" );
document.write( "

\n" ); document.write( "b) only who sits next to whom counts, but not on which side (rotations and reflections do not change the arrangement)?
\n" ); document.write( "
\r\n" );
document.write( "Each seating arrangement in part (a) has one reflection, so we divide that answer\r\n" );
document.write( "by 2 and get 252.  \r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );