Question 227351
Jasmine says that there are 362,880 distinguishable permutations of the letters in the word TEXTBOOKS. Do you agree? 
<pre><font size = 4><b> 
If the T's and the O's were distinguishable, say one of them
were red and the other blue, different colore,
like this: 

<font color="red">T</font>EX<font color="blue">T</font>B<font color="red">O</font><font color="blue">O</font>KS

there would be 9! ways, and then 352,880 would be correct.

However, let's look at one of those.

K<font color="red">O</font>BX<font color="blue">T</font>SE<font color="red">T</font><font color="blue">O</font>

The 9! counts these 4 separately:

K<font color="red">O</font>BX<font color="blue">T</font>SE<font color="red">T</font><font color="blue">O</font>
K<font color="blue">O</font>BX<font color="blue">T</font>SE<font color="red">T</font><font color="red">O</font>
K<font color="red">O</font>BX<font color="red">T</font>SE<font color="blue">T</font><font color="blue">O</font>
K<font color="blue">O</font>BX<font color="red">T</font>SE<font color="blue">T</font><font color="red">O</font>

and similarly every permutation is counted 4 times. However all
the letters are the same color, and so these 4 cannot be told
apart.  So we have to divide the 9! by 4 to get the number of
distinguishable permutations.  So the answer is not 362880 at
all.  It's

{{{9!/4 = 362880/4 = 90720}}}

Edwin</pre>