Question 1095620
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How many distinguishable permutations can be made of the letters in the word STEGOSAURUS? 
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<pre>
The given word contains  11  letters.


Of them, the letter S  is repeated 3 times,   and
         the letter U  is repeated 2 times.


The rest of the letters are unique.


So, the number of  distinguishable permutations  is  {{{11!/(3!*2!)}}} = 3326400.
</pre>

We divide the total number of permutations of 11! by 3!, because all permutations that permute the letter S only, lead to  indistinguishable arrangements.


We divide the total number of permutations of 11! by 2!, because all permutations that permute the letter U only, lead to  indistinguishable arrangements, too.



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On Permutations, see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Permutations.lesson>Introduction to Permutations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/PROOF-of-the-formula-on-the-number-of-permutations.lesson>PROOF of the formula on the number of Permutations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Problems-on-Permutations.lesson>Problems on Permutations</A>

in this site.