Question 541020
<pre>
If we could tell the two d's apart, and the three e's apart, and the
word were written like this:

decrE&#5486;D

then the answer would be 7! = 5040

However if we take a random permutation of that, say

c&#5486;DerdE

There are 3! ways to arrange the &#5486;, e, and E within that permutation,
and every other permutation of decrE&#5486;D is the same way, so that
means that the 7! or 5040 counts the same permutation 3! of 6 times too
many, so we must divide by 3! or 6.

But there are also 2! ways the D and d can be arranged, so we must
also divide by 2!, since we cannot tell the D from the d when they are
both small d's.  Therefore the number of distinguishable ways when
all the e's look alike and both the d's look alike, is given by

{{{7!/(3!2!)}}} = {{{5040/(6*2)}}} = {{{5040/12}}} = 420    
   
Edwin</pre>