SOLUTION: Find the number of distinguishable permutations of the letters of the word EDUCATED.

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Question 1016893: Find the number of distinguishable permutations of the letters of the word EDUCATED.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the word is educated.

without any duplicates the number of permutations would be 8! because there are 8 letters.

since 2 of the letters are duplicates, the formula becomes 8! / (2! * 2!) = 8! / 4

since 8! = 8*7*6*5*4*3*2*1, then 8! = 40320

8! / 4 becomes 40320 / 4 = 10080.

here's a good reference.

http://www.regentsprep.org/regents/math/algebra/apr2/LpermRep.htm