SOLUTION: Find the number of distinguishable permutations of the given letters "AAABBBCD".

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Question 1204716: Find the number of distinguishable permutations of the given letters "AAABBBCD".
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
permutations of { ,, , , ,, , }
there are letters
there are s and s, since order matters, there will be following number of permutations :

/(**....*)


Distinct subsets:
Subsets : ; ; ; ;
Subsets' count: , , ,


The letters of the word can be arranged in distinct ways.


Answer by ikleyn(52921)   (Show Source): You can put this solution on YOUR website!
.
Find the number of distinguishable permutations of the given letters "AAABBBCD".
~~~~~~~~~~~~~~~~~~~~~~~~~ 

The formula for the number of distinguishable permutations of this word is

    n = .    (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  ANSWER  is, according to formula (1),  n = 1120.

Solved.

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To see many other similar  (and different)  solved problems,  look into the lesson
    - Arranging elements of sets containing indistinguishable elements
in this site.

Learn the subject from there.



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