SOLUTION: How many different​ 10-letter words​ (real or​ imaginary) can be formed from the following​ letters? E,T,J,N,M,N,T,F,G,P

Algebra ->  Permutations -> SOLUTION: How many different​ 10-letter words​ (real or​ imaginary) can be formed from the following​ letters? E,T,J,N,M,N,T,F,G,P      Log On


   

Question 1143068: How many different​ 10-letter words​ (real or​ imaginary) can be formed from the following​ letters?
E,T,J,N,M,N,T,F,G,P
Answer by ikleyn(52914) About Me  (Show Source):
You can put this solution on YOUR website!
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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%21%2F%282%21%2A2%21%29 = %2810%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%282%2A2%29 = 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".


ANSWER.  The number of all distinguishable 10-letter arrangements of the given 10 letters is  907200.

Solved.

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    - Arranging elements of sets containing indistinguishable elements
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