  Quantum coherence is the outcome of the superposition principle. Recently, it
has been theorized as a quantum resource, and is the premise of quantum
correlations in multipartite systems. It is therefore interesting to study the
coherence content and its distribution in a multipartite quantum system. In
this work, we show analytically as well as numerically the reciprocity between
coherence and mixedness of a quantum state. We find that this trade-off is a
general feature in the sense that it is true for large spectra of measures of
coherence and of mixedness. We also study the distribution of coherence in
multipartite systems by looking at monogamy-type relation--which we refer to as
additivity relation--between coherences of different parts of the system. We
show that for the Dicke states, while the normalized measures of coherence
violate the additivity relation, the unnormalized ones satisfy the same.
