  We study the correlation dynamics of a system composed of arbitrary numbers
of qutrits interacting with a common environment. Initially, the system is
assumed to be in a low dimensional subspace of the Hamiltonian called
"decoherence-free subspace". Environment induced quantum entanglement and
discord is calculated between pair of qutrits of the system as measures of
non-classical correlations. Finally the steady state distribution of
entanglement and discord is determined with respect to the total number of
qutrits of the system.
