Why are paramagnetic materials attracted to ferrimagnetic materials(such as iron, nickel, and cobalt)?
First of all, in your question i feel a confusion about the nature of magnetism and paramagnetism. These magnetic interactions have nothing to do with attraction/repulsion of electric charges, and magnets do not attract or repel Coulomb charges (when we discuss the magnetic part of the interaction). In short static, magnetic and electric properties are two different stories.

Second, iron is ferrOmagnetic and not ferrImagnetic (capitalisation is by me). Forget ferrimagnetic materials for a second, and let's just talk about ferromagnetic, paramagnetic and diamagnetic materials: 


Diamagnetic materials have no free electronic spin in the system, therefore they do not interact with magnetic field as a first approximation. There is a very small repulsive interaction coming from the polarisation of paired spins, but it is very small compared to any other interactions. Most organic compounds are in this category.
Paramagnetic materials have free electronic spins, which can flip / rotate. When put the sample in magnetic field, this field polarises the spins which turns into an attractive interaction. This is analogous with the electric field induced dipole moments, but this is a magnetic interaction, not an electronic interaction. The alignment of spins are constantly changing, as simple thermal excitation can rotate them. Therefore paramagnetic materials has no permanent magnetic moments like magnets. Typical examples are molecular oxygen, transition metal complexes, etc. 
In ferromagnetic materials the free electronic spins are having a strong interaction with each other, and aligned parallel in strict order. This alignment is so stable that the magnetic moment of spins adds up, and there can be a macroscopical magnetic field around the sample (i.e. it is a magnet). 


When you see the attraction between paramagnetic and magnetic materials, you see the polarisation of the paramagnetic materials in the magnetic field of ferromagnetic materials, which is an attractive itneraction.