= Size of a type class
{title2=$|T_n(q)|=n!/\prod_a(nq(a))!$}
Write $n_a=nq(a)$. Arranging $n_a$ copies of each symbol gives the <multinomial coefficient>
$$
\boxed{|T_n(q)|=\frac{n!}{\prod_{a\in\mathcal A}n_a!}.}
$$
The division by the <factorials> removes permutations among identical copies. In the balanced four-symbol example, $|T_4(q)|=4!/(2!2!)=6$. For binary symbols this becomes the <binomial coefficient> $\binom nk$; for three symbols with counts $(2,1,1)$, the class contains $4!/(2!1!1!)=12$ strings.
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