Unitary evolution to a state with a fixed mean number of particles

In the framework of finite-dimensional Fock space models, for a predefined fixed mean number of particles $\bar{n}_{k}$, it is shown that there is a ``large'' multi-dimensional subspace $s_{\bar{n}_{k}}$ of initial pure states, in the space $S$ of all pure states, unitarily evolving to a subspace $S_{\bar{n}_{k}}$ of final pure states which yield $\bar{n}_{k}$. As an example, in particular it follows that the blackbody form of the mean number of particles $\bar{n}_{k}$ does not by itself contradict unitarity of black hole evaporation.