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Rich experimental data accumulated in the past few years in the hadronic$Z^0$ decays allow one to check the quark combinatorics relations for a newtype of processes, namely: quark jets in the decays $Z^0 \to q\bar q \tohadrons$. In this paper we review quark combinatorics rules for the yields ofvector and pseudoscalar mesons, $V/P$, in the central and fragmentation regionsof the hadronic $Z^0$ decays. It is stressed that in the central region adirect verification of quark combinatorics rules is rather problematic becauseof a considerable background related to the decay of highly excited resonances;however such a verification is possible in the fragmentation region, at$x_{hadron} \sim 0.5-1$, where the contribution of resonance decays issuppressed due to the rapid decrease of spectra with increasing $x_{hadron}$.It is shown that the experimental data in the fragmentation region for$\rho^0/\pi^0$ and $p/\pi^+$ are in a reasonable agreement with the predictionsof quark combinatorics. The ratios of the heavy meson yields, $B^*/B$ and  $D^*/D$, are also discussed: the data demonstrate a good agreement with thequark combinatorial results. We analyse the structure of the suppressionparameters for strange and heavy quark productions in soft processes andestimate their order of magnitudes in the multiperipheral processes; the ratio$K^{\pm}/\pi^{\pm}$ at $x_{hadron}\sim 0.5-0.8$ and production probabilities ofthe $c\bar c$ and $b \bar b$ mesons are in a good agreement with the estimates.Comment: 28 pages, LaTeX, 7 figures, epsfig.sty, corrected some typo

Quark combinatorics and meson-production ratios in hadronic Z 0 decays