While preparing for an exam I found a problem where one has to find the composition of hadrons given their quantum numbers.

$$\text{ (Charge, Baryon number, Strangeness, Charm, Bottomness)=(Q,B,s,c,b)}$$

We know that (source: hyperphysics):
$Q_s=-\frac{1}{3}$, $S =-1$, $Q_b=-\frac{1}{3}$, $B=-1$, $Q_c=+\frac{2}{3}$, baryon number = $\frac{1}{3}(n_q-\overline{n}_q)$,
$n_q$ and $\overline{n}_q $ being respectively the number of quarks and anti-quarks.

However there is one particle that shouldn't exist which is: $$\text{(2,1,0,1,0)}$$ This Hadron has to consist of $ccc$, since it's the only possible way to achieve a charge of $2$ given our three quarks.
However, I'm confused why it isn't $(2,1,0,3,0)$, since there are three charm quarks with $c=1$ for each one, mounting to $3$.
Any help is appreciated.


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