How many deranged anagrams exist of the word memes so that no letter ends up in its original position and no letter ends up in the original position of an identical letter.

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.CR: Chapter Review
Problem 70E: How many distinguishable words can be formed from the letters of the word casserole if each letter...
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How many deranged anagrams exist of the word memes so that no letter ends up in its original position and no letter ends up in the original position of an identical letter. 

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There are 30 total anagrams of the word memes. I listed all 30 and could only find 4 deranged anagrams. Why is it 11 and not 4? The only 4 I could find are EMSME, ESEMM< SMEME, EMESM

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