document.write( "Question 1200454: In how many ways can 3 Americans, 4 Frenchmen, 4 Danes and 2 Italians be seated in a round table if those of the same nationality sit together? \n" ); document.write( "

Algebra.Com's Answer #834597 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "In how many ways can 3 Americans, 4 Frenchmen, 4 Danes and 2 Italians be seated
\n" ); document.write( "in a round table if those of the same nationality sit together?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "We have 4 blocks of people according their nationalities.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "4 items (4 blocks, in this case) can be placed around a circle in  (4-1)! = 3! = 1*2*3 = 6 different ways.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(Using mathematical language, for n different objects, there are (n-1)! different circular permutations).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next, there are 3! =  6 permutations inside the block of Americans,\r\n" );
document.write( "                4! = 24 permutations inside the block of Frenchmen,\r\n" );
document.write( "                4! = 24 permutations inside the block of Danes, and\r\n" );
document.write( "                2! =  2 permutations inside the block of Italians.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, there are 6*(6*24*24*2) = 41472 different placements under imposed conditions.    ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-----------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "To see many other similar (and different) solved problems, look into the lesson\r
\n" ); document.write( "\n" ); document.write( " - Persons sitting around a cicular table \r
\n" ); document.write( "\n" ); document.write( "in this site, and learn the subject from there.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );