document.write( "Question 1147173: There are two round tables, one oak and one mahogany, each with five seats. In how many ways may a group of ten people be seated? \n" ); document.write( "

Algebra.Com's Answer #768521 by ikleyn(52778) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "So we have 5 persons around each table.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The key fact in the solution is that if there are N people, then there are (N-1)! distinguishable ways \r\n" );
document.write( "to place them around the round table.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    These are so called \"circular\" permutations, in distinct from usual permutations, \r\n" );
document.write( "\r\n" );
document.write( "    where  N!  regular permutations exist for N objects.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "After this introduction, I am ready now to present the solution.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "1)  You can select 5 persons from 10 to place them around first table (team 1) by   =  = 252 ways.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    As soon as your team 1 is just formed, team 2 (for the second table) is formed automatically - they are remaining 5 people.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "2)  You can place 5 members of the team 1 around Table 1 by 4! = 24 ways.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "3)  You can place 5 members of the team 2 around Table 2 by 4! = 24 ways.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "4)  Thus the total number of different ways is the product\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "         * 4! * 4! = 252 * 24 * 24.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Use your calculator to get the required number.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );