I wasn't expecting that .......

Probability Level 5

Suppose we have 88 distinct containers and 88 indistinguishable balls. The balls are then distributed into the containers such that the distribution is uniform across all possible events. That is, each distribution (a1,a2,a3,a4,a5,a6,a7,a8)(a_{1},a_{2},a_{3},a_{4},a_{5},a_{6},a_{7},a_{8}) of balls, where ana_{n} is the number of indistinguishable balls in the nnth container such that n=18an=8\sum_{n=1}^8 a_{n} = 8, is equally likely to occur.

The expected number of containers that have at least one ball in them is ab\frac{a}{b}, where aa and bb are positive coprime integers. Find a+ba + b.

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