SOLUTION: 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 pos

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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?
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
That depends on whether, say, these three table
seating arrangements
   
 ____________     ____________    ____________   
| Tom   Ann  |   | Meg   Tom  |  | Meg   Sam  |  
|            |   |            |  |            |      
|            |   |            |  |            |    
|_Sam___Meg__|   |_Ann__Sam___|  |_Ann__Tom___|  


are considered as three DIFFERENT seating arrangements or whether
they are considered to all three be the SAME seating arrangement:

If the three above are considered to be DIFFERENT seating arrangements, 
then there are 16 seats to place 16 students, so the answer is
16! = 16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1 = 2.09x10^13

But if those are considered to all be the same seating arrangement
(because they can take any of the four seats at the tables) then 
the answer is

(16C4)(12C4)(8C4)(4C4) = (1820)(495)(70)(1) = 63,063,000

Edwin
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