SOLUTION: A band has 4 trumpets, 3 trombones, 3 saxophones & 2 drums. If each section has its own set of seats, in how many ways can the 12 band members be seated?

A band has 4 trumpets, 3 trombones, 3 saxophones & 2 drums. If 
each section has its own set of seats, in how many ways can the 
12 band members be seated?

Instruments:   TRUMPETS      TROMBONES    SAXOPHONES     DRUMS
Seats:           ABCD           EFG          HIJ          KL

We can choose who sits in seat A any of 4 ways, so far that's 
4 ways, then
We can choose who sits in seat B any of 3 ways, so far that's    
4·3 ways, then
We can choose who sits in seat C any of 2 ways, so far that's      
4·3·2 ways, then
We can choose who sits in seat D only 1 way, so far that's        
4·3·2·1 ways, then
We can choose who sits in seat E any of 3 ways, so far that's   
4·3·2·1·3 ways, then
We can choose who sits in seat F any of 2 ways, so far that's  
4·3·2·1·3·2 ways, then
We can choose who sits in seat G only 1 way, so far that's  
4·3·2·1·3·2·1 ways, then
We can choose who sits in seat H any of 3 ways, so far that's  
4·3·2·1·3·2·1·3 ways, then
We can choose who sits in seat I any of 2 ways, so far that's  
4·3·2·1·3·2·1·3·2 ways, then
We can choose who sits in seat J only 1 way, so far that's  
4·3·2·1·3·2·1·3·2·1 ways, then
We can choose who sits in seat K any of 2 ways, so far that's  
4·3·2·1·3·2·1·3·2·1·2 ways, then
We can choose who sits in seat L only 1 way, so far that's 
4·3·2·1·3·2·1·3·2·1·2·1 ways.

Thats 1728 ways.

Edwin
AnlytcPhil@aol.com