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.