I'm assuming that what you have here is the following model. Here I'll only handle the case of one single team.
Let $ X_i \sim \text{Bernoulli}(p_i) $, where $ X_i = 1 $ when person $ i $ shows up to work, and $ X_i = 1 $ with probability $ p_i $.
Then, let $ N $ be the size of the team, and let $ Y = \sum_{i=1}^N X_i $.
Then, $ Y $ is the number of people on the team that show up in case of a flood.
What you're interested in now is the probability mass function of $ Y $,
i.e. $ P(Y = k)\,, k = \{1, \cdots, N\} $.
If $ p_i = p $ for each individual on the team, then $ Y $ is simply
a Binomial($N, p$) random variable. But it sounds like here that the
$ p_i $'s are allowed to be different.
In this case, this is still computable (but naively intractable, not sure if there is
an efficient algorithm to compute this).
Consider, for example $ P(Y = 1) $. This is the probability that one person shows up. We have that
\begin{equation}
\begin{aligned}
P(Y = 1)
& = \sum_{i=1}^N P(\text{person $ i $ shows up and no one else does})\\
& = \sum_{i=1}^N p_i \prod_{j \in \{1, \cdots, N\}, j \neq i} (1 - p_j)
\end{aligned}
\end{equation}
and then follow this same logic for $ P(Y = k), k \in \{1, \cdots, N\} $.
For large $ N $ or small $ p_i $'s, you may want to do this computation
on log-probabilities.
