Which type of bacterial cell grouping results from division in random planes?

The type of bacterial cell grouping that results from division in random planes is indeed the cluster formation. When bacteria divide by binary fission, the division can occur in different orientations. In the case of clustering, the cells divide in multiple planes and do not follow a specific arrangement, leading to a three-dimensional grouping of cells known as a cluster or “coccus” arrangement. This can be observed in bacteria such as Staphylococcus, where the cells appear in irregular grape-like clusters due to their random division orientations.

Chain arrangements typically involve division along one plane, leading cells to remain connected in a linear fashion, as seen in Streptococcus. The term "pact" is not a standard term used in microbiology to describe any form of bacterial arrangement, and "stab" does not pertain to cell division patterns but rather can refer to a method of inoculation in a solid medium. Thus, the characteristics of the cluster formation set it apart as the correct answer in relation to random divisions.