Louis Armstrong – Summertime chords

Hi everyone! I am not sure these chords are right, but it sounds exactly like in 
the song. Hope you like it!
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    Am    E                 AmSummertime, and the living is easy, 

    Dm                          EFish are jumping and the cotton is high. 
 
Am                E                  AmYour daddy is rich and your mummy is good lookin', 
 
   C                    E       AmSo hush, little baby, don't you cry. 

   Am                 E                       AmOne of these mornings you'll gonna rise up singin', 
 
   Dm                              E  Then you'll spread your wings and you'll take the sky.

   Am                 E                    AmBut till that morning there's nothing can harm you, 

     C                      E         AmWith daddy and mammy, mammy standing by.