Question 314210
<pre><b>
If the three E's were colored difference, like this

D<font color = "red">E</font>F<font color = "blue">E</font>NS<font color = "green">E</font>, the answer would be 7P7 or 7! since there are 7 letters.
However, for example take the arrangement:

SNEFEED

If the E's were colored differently and we could tell the difference 
then we could rearrange the colored E's around and the following 6 
would all be different:

SN<font color = "red">E</font>F<font color = "blue">E</font><font color = "green">E</font>D
SN<font color = "red">E</font>F<font color = "green">E</font><font color = "blue">E</font>D
SN<font color = "blue">E</font>F<font color = "red">E</font><font color = "green">E</font>D
SN<font color = "blue">E</font>F<font color = "green">E</font><font color = "red">E</font>D
SN<font color = "green">E</font>F<font color = "red">E</font><font color = "blue">E</font>D
SN<font color = "green">E</font>F<font color = "blue">E</font><font color = "red">E</font>D

The reason there are 6 is because there are 3P3 = 3! ways the E's can
be rearranged as above.  So the answer 7! = 5040 is too large a numbee
because every arrangement is counted 3! = 6 times too many.  So we must
divide 7! by 3! to get the correct answer.  So the answer is

{{{7!/3!=(7*6*5*4*3*2*1)/(3*2*1)=(7*6*5*4*cross(3*2*1))/(cross(3*2*1))=7*6*5*4=840}}}  

Edwin</pre>