SOLUTION: A student has 5 engineering books, 3 math books, and 4 chemistry books. She is to put them all onto three shelves (top, middle, lower) with each shelf containing only books of a si

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Question 944565: A student has 5 engineering books, 3 math books, and 4 chemistry books. She is to put them all onto three shelves (top, middle, lower) with each shelf containing only books of a single discipline, but the order on any particular shelf is completely free. In how many ways can she do this ?
I'm stuck here, it seems easy enough, but why would the number of books matter if each shelf contains one discipline and the order on each shelf doesn't matter? Am I missing something here?
It looks along the lines of 5!*3!*4!*3!, but not sure.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
No, you're right about the number of books.  The answer is just 6.
Here's why.

The books of each discipline are NOT ordered, However the shelves 
ARE ordered (top. middle, lower)

We have some engineering books, some math books, and some chemistry books.
You are right that it doesn't matter how many of each, so the 5,3, and 4 have
nothing to do with the problem.  They're just to throw you off.

So the answer is just 3! or 6.

Here are the 6 ways
                 1    2    3    4    5   6
------------------------------------------     
top shelf       5E   5E   3M   3M   4C  4C
------------------------------------------    
middle shelf    3M   4C   5E   4C   5E  3M
------------------------------------------
lower shelf     4C   3M   4C   5E   3M  5E
------------------------------------------

Edwin