Show that the if space, spin, and flavor are assumed to be the operative degrees of freedom for particles in the baryonic \(\mathbf{1 0}\) of Fig. 9.1 (d), the ground states for the spin- \(\frac{3}{2}\) baryons are in conflict with the Pauli principle (which requires a fermionic wavefunction to be totally antisymmetric). Assume an additional degree of freedom (color) associated with a new SU(3) symmetry of the quarks that is independent of flavor \(\mathrm{SU}(3)\), with the quarks transforming as fundamental representations under the color SU(3) symmetry. Show that the Pauli principle can now be satisfied if the particles of the baryon decuplet transform as a \(\mathbf{1 0}\) with respect to flavor \(\mathrm{SU}(3)\) but as a 1 with respect to color \(\mathrm{SU}(3)\).