document.write( "Question 1067291: A group of 3 English majors, 2 anthropology majors, and 5 history majors are going out to dinner, where they will sit at a circular table.\r
\n" ); document.write( "\n" ); document.write( "If students with the same major need to sit together, how many different ways can the students be seated around the table?\r
\n" ); document.write( "\n" ); document.write( "There are __[blank]__ different ways the students can be seated around the table. \n" ); document.write( "
Algebra.Com's Answer #684449 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "I've never known why, but problems involving circular tables are the\r\n" );
document.write( "same as if we had the unrealistic situation where the table, chairs, \r\n" );
document.write( "and people were on a large revolving platform and the table, chairs,\r\n" );
document.write( "and people rotated at different angles would not be considered \r\n" );
document.write( "different arrangements.  \r\n" );
document.write( "\r\n" );
document.write( "We can choose the seating order of the English majors 3!=6 ways, the \r\n" );
document.write( "seating order of the anthropology majors 2!=2 ways, and the seating \r\n" );
document.write( "order of the history majors 5!=120 ways. \r\n" );
document.write( "\r\n" );
document.write( "That's (6)(2)(120)=1440 ways.\r\n" );
document.write( "\r\n" );
document.write( "If the 3 groups were in a straight line they could be arranged in\r\n" );
document.write( "3!=6 ways, but since the table is considered to be on a turntable, \r\n" );
document.write( "there are only 2!=2 ways. [They are English, anthropology, history, \r\n" );
document.write( "or English, history, anthropology. Any other order of the major \r\n" );
document.write( "subjects could be had by rotating the imaginary turntable.]\r\n" );
document.write( "\r\n" );
document.write( "Answer: 1440*2 = 2880 ways.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );