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I'm trying to find the exponential generating function for the numbers of ways to distribute $r$ distinct objects into five different boxes when $b_1 < b_2 \leq 4$, where $b_i$ denotes the number of objects in the $i$-th box. I know how to find a exponential generating function in general, but I don't understand how to handle the constraint that $b_1 < b_2$. It seems this would change what I could use to generate $b_1$ for each possible $b_2$. Any hint on how to deal with this complication would be appreciated.

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    What is $b_1$ and $b_2$?2012-04-17

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