Creating multiparticle states from vacuum in QFT

In creating multiparticle states from the vacuum we apply the creation operators,
begin{align}
&|p_1,s_1rangle=a^{dagger}_{p_1,s_1}|0rangle,
&|p_1,s_1;p_2,s_2rangle=a^{dagger}_{p_1,s_1}a^{dagger}_{p_2,s_2}|0rangle,
& …quad …quad …quad …quad …quad …
&|p_1,s_1;p_2,s_2;…,,…;p_n,s_nrangle=a^{dagger}_{p_1,s_1}a^{dagger}_{p_2,s_2}…,…, …a^{dagger}_{p_n,s_n}|0rangle
qquad qquad text{etc.}
end{align}

for particles having momentum $p$ and spin $s$. Some authors also include combinatorial prefactors like $frac{1}{sqrt{2!}}$, … $frac{1}{sqrt{n!}}$ on the r.h.s. My question is that is it just a convention, to be compensated later by some other similar normalization prefactor, e.g. in the definition of inner product, amplitude, etc? Or does it have a concrete physical reason, in order to incorporate the indistinguishability of fermions/bosons, since the ordering of the creation-operators is ambiguous up to a sign?