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

**Discrete Mathematics**Level 5

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 \(a + b\).