Final answer:
A nucleosome does not contain histones H1 in its core; it consists of an octamer of histones - two each of H2A, H2B, H3, and H4, with H1 as a linker, so the statement is false.
Step-by-step explanation:
The statement that a nucleosome contains two molecules each of histones H1 and H2A, H2A and H2B is false. Each nucleosome consists of a core of eight histone proteins, which includes two copies each of H2A, H2B, H3, and H4. These eight histones form an octamer around which DNA is tightly wrapped to create the nucleosome structure. Separate from this core, histone H1 is involved in linking the nucleosomes together and stabilizing the structure but is not part of the core nucleosome itself. The DNA is wrapped around the histone proteins to form nucleosome complexes, which appear like beads on a string under an electron microscope.