Question 1143068
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<pre>

There are 10 letters in the given set; of them, two letters "T" are identical and two letters "N" are identical.


Therefore, the number of all distinguishable 10-letter arrangements of the given 10 letters is  {{{10!/(2!*2!)}}} = {{{(10*9*8*7*6*5*4*3*2*1)/(2*2)}}} = 907200.


In the formula,  the first  2! in the denominator stands to account for repeating letter "T".


The other 2! in the denominator stands to account for repeating letter "N".


<U>ANSWER</U>.  The number of all distinguishable 10-letter arrangements of the given 10 letters is  907200.
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Solved.


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See the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/Arranging-elements-of-sets-containing-undistinguishable-elements.lesson>Arranging elements of sets containing indistinguishable elements</A> 

in this site.