Question 1143786
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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.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The correct formulation is <U>THIS</U> :


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                What is the number of all distinguishable arrangements of the letters in the word ASSASSIN ?
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<U>SOLUTION</U>


<pre>
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 <U>distinguishable</U> arrangements is  


    8!/(2!*4!) = {{{(1*2*3*4*5*6*7*8)/(2*24)}}} = 840.    <U>ANSWER</U>


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".
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