Question 944565
<pre>
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</pre>