According to the founders of quantum mechanics and quantum biology P. Jordan and E. Schrödinger, the main difference between living and inanimate objects is the dictatorial influence of genetic molecules on the whole living organism. Code biology can make a valuable contribution to understanding this dictatorial influence of genetic molecules whose ensemble is endowed with many interconnected alphabets and codes. The paper is devoted to probability rules of nucleotide sequences of single-stranded DNA in eukaryotic and prokaryotic genomes. These rules are connected with n-plets alphabets of DNA whose nucleotide sequences are considered as bunches of many parallel texts written in interconnected n-plets alphabets. The rules draw attention to genomic phenomena of special tetragroupings of n-plets and new genomic symmetries. A generalization of the second Chargaff's rule is described. They show the existence of long-range coherence in genomic DNA sequences and reveal new connections of structural features of genomic sequences with formalisms of quantum mechanics and quantum informatics. The author supposes that the received results are related to the known vibration-resonance theory of G. Frohlich about long-range coherence in biological systems, that is, about collective quantum effects there. The possible influence of the described genetiс probability phenomena on the genetically inherited physiological structures is noted and discussed. Copyright © 2021 Elsevier B.V. All rights reserved.