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

Suppose we have $$8$$ distinct containers and $$8$$ indistinguishable balls. The balls are then distributed into the containers such that the distribution is uniform across all possible events. That is, each distribution $$(a_{1},a_{2},a_{3},a_{4},a_{5},a_{6},a_{7},a_{8})$$ of balls, where $$a_{n}$$ is the number of indistinguishable balls in the $$n$$th container such that $$\sum_{n=1}^8 a_{n} = 8$$, is equally likely to occur.

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

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