SOLUTION: what is the permutations of the letters in the word of ASSASSIN?

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Question 1143786: what is the permutations of the letters in the word of ASSASSIN?
Answer by ikleyn(52780) About Me  (Show Source):
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what is the permutations of the letters in the word of ASSASSIN?
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            The original formulation in the post is INCORRECT.

            The correct formulation is THIS : 

                What is the number of all distinguishable arrangements of the letters in the word ASSASSIN ?


SOLUTION 

The given word has 8 symbols.


Of these 8 symbols, the letter "A" repeats 2 times, and the letter "S" repeats 4 times.


All other letters are distinct and unique.


The number of all permutations of 8 symbols is 8!


But the number of all distinguishable arrangements is  


    8!/(2!*4!) = %281%2A2%2A3%2A4%2A5%2A6%2A7%2A8%29%2F%282%2A24%29 = 840.    ANSWER


In the formula,  2!  in the denominator stands to account for repeating letter "A", 

           while 4! in the denominator stands to account for repeating letter "S".