Question 891440
<pre>
The formula for the number of distinguishable arrangements is:

{{{matrix(1,10,

The,factorial,of,the,number,of,letters,in,the,word)/

matrix(1,17,

The,product,of,the,factorials,of,the,number,of,times,each,indistinguishable,
letter,appears,in,the,word)}}}

INDEPENDENCE has 12 letters, so 12! is the numerator.
There are 3 indistinguishable N's, so one of the factors of the denominator is 3!
There are 2 indistinguishable D's, so one of the factors of the denominator is 2!
There are 4 indistinguishable E's, so one of the factors of the denominator is 4!

Answer: {{{12!/(3!2!4!)}}}{{{""=""}}}{{{1663200}}}

Edwin</pre>