= Solution
The $\Delta^{++}$ <Delta baryon> has <electric charge> $+2$ and <valence quark> content $uuu$. In its ground state the spatial wavefunction has orbital <angular momentum> $L=0$ and is symmetric. Its <spin> is $3/2$; the maximal projection state $u_\uparrow u_\uparrow u_\uparrow$ is symmetric in <spin>, and its <quark flavour> wavefunction is symmetric as well. Three identical <fermions> require an antisymmetric total wavefunction by the <Pauli exclusion principle>. A further internal degree of freedom must therefore supply the antisymmetry.
With three <color charges>, that factor is the normalized <colour singlet>
$$
\boxed{|C\rangle=\frac{|rgb\rangle+|gbr\rangle+|brg\rangle-|rbg\rangle-|grb\rangle-|bgr\rangle}{\sqrt6}.}
$$
It changes sign under exchange of any two <quarks>. The remaining symmetric factors then give the required antisymmetric total state. This argument motivates <color charge> independently of the already present <quark flavour> and <spin> labels.
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