Given a suitable collection of partitions of sets, there exists a connection to easy quantum groups via intertwiner maps. A sufficient condition for this correspondence to be one-to-one are particular linear independences on the level of those maps. In the case of non-crossing partitions, a proof of this linear independence can be traced back to a matrix determinant formula, developed by W. Tutte. We present a revised and adapted version of Tutte's work and the link to the problem above, believing that this self-contained article will assist others in the field of easy quantum groups. In particular, we fixed some errors in the original work and adapted notations, definitions, statements and proofs.