Question: Suppose I throw 10 balls into 5 bins labeled A,B,C,D,E uniformly at random. Call a pair of bins special if they are labeled with adjacent

Suppose I throw 10 balls into 5 bins labeled A,B,C,D,E uniformly at random. Call a pair of bins special if they are labeled with adjacent letters (i.e., the pairs AB, BC, CD, DE are special). The expected number of special pairs of bins which are both empty is:

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