Final answer:
Histone H1 is likely the molecule removed or mutated because it is essential for the packing of nucleosomes into the 30-nm chromatin fiber, which is absent in the cell in question.
Step-by-step explanation:
If a cell can form 10-nm chromatin fibers but not 30-nm fibers, the molecule likely removed or mutated is histone H1. This is because histone H1 is involved in the higher-order packing of nucleosomes into the 30-nm chromatin fiber. As nucleosomes are coiled into a 30-nm fiber, histone H1 plays a crucial role in this level of compaction, helping to facilitate the transition from the 'beads on a string' appearance of the nucleosomes to the more compact structure. Without H1, the DNA would be unable to achieve the condensation necessary to form the solenoid structure of the 30-nm fiber.