Question 1204716
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Find the number of distinguishable permutations of the given letters "AAABBBCD".
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<pre>
The formula for the number of distinguishable permutations of this word is

    n = {{{8!/(3!*3!)}}}.    (1)


In this formula, 8! reflects the number of all permutations of 8 letters in the word.

First  3!  in the denominator reflects three repeating letters A in it.

Second 3!  in the denominator reflects three repeating letters B in the word.


The  <U>ANSWER</U>  is, according to formula (1),  n = 1120.
</pre>

Solved.


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To see many other similar &nbsp;(and different) &nbsp;solved problems, &nbsp;look into 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.


Learn the subject from there.