document.write( "Question 438918: A teacher is making a seating chart for a class of 16 students. If each student is assaigned to one of 4 tables that seat 4 students each, how many different seating charts are possible? \n" ); document.write( "
Algebra.Com's Answer #303412 by Edwin McCravy(20054)![]() ![]() You can put this solution on YOUR website! \r\n" ); document.write( "That depends on whether, say, these three table\r\n" ); document.write( "seating arrangements\r\n" ); document.write( " \r\n" ); document.write( " ____________ ____________ ____________ \r\n" ); document.write( "| Tom Ann | | Meg Tom | | Meg Sam | \r\n" ); document.write( "| | | | | | \r\n" ); document.write( "| | | | | | \r\n" ); document.write( "|_Sam___Meg__| |_Ann__Sam___| |_Ann__Tom___| \r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "are considered as three DIFFERENT seating arrangements or whether\r\n" ); document.write( "they are considered to all three be the SAME seating arrangement:\r\n" ); document.write( "\r\n" ); document.write( "If the three above are considered to be DIFFERENT seating arrangements, \r\n" ); document.write( "then there are 16 seats to place 16 students, so the answer is\r\n" ); document.write( "16! = 16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1 = 2.09x10^13\r\n" ); document.write( "\r\n" ); document.write( "But if those are considered to all be the same seating arrangement\r\n" ); document.write( "(because they can take any of the four seats at the tables) then \r\n" ); document.write( "the answer is\r\n" ); document.write( "\r\n" ); document.write( "(16C4)(12C4)(8C4)(4C4) = (1820)(495)(70)(1) = 63,063,000\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |