Quantum correlations (QCs) in some separable states have been proposed as a key resource for certain quantum communication tasks and quantum computational models without entanglement. In this paper, a family of nine-parameter separable states, obtained from arbitrary mixture of two sets of bi-qubit product pure states, is considered. QCs in these separable states are studied analytically or numerically using four QC quantifiers, i. e., measurement-induced disturbance (Luo in Phys Rev A77: 022301, 2008), ameliorated MID (Girolami et al. in J Phys A Math Theor 44: 352002, 2011), quantum dissonance (DN) (Modi et al. in Phys Rev Lett 104: 080501, 2010), and new quantum dissonance (Rulli in Phys Rev A 84: 042109, 2011), respectively. First, an inherent symmetry in the concerned separable states is revealed, that is, any nine-parameter separable states concerned in this paper can be transformed to a three-parameter kernel state via some certain local unitary operation. Then, four different QC expressions are concretely derived with the four QC quantifiers. Furthermore, some comparative studies of the QCs are presented, discussed and analyzed, and some distinct features about them are exposed. We find that, in the framework of all the four QC quantifiers, the more mixed the original two pure product states, the bigger QCs the separable states own. Our results reveal some intrinsic features of QCs in separable systems in quantum information.