Because only a small number of B cells recognize a given antigen, an activated B cell divides repeatedly by mitosis to form a large clone.
Clonal expansion supplies enough plasma cells to secrete an effective quantity of one antibody type. Every plasma cell in the clone inherits the selected antibody specificity.
Rare matching B cell → activation → repeated mitosis → clone of genetically matching cells → many plasma cells secrete the same specific antibody; some cells can become memory cells.
A selected B cell responding to a bacterial surface antigen produces thousands of plasma-cell descendants, all releasing antibodies complementary to that antigen.
Antibodies are secreted in quantity by differentiated plasma cells, not by every inactive B cell. Mitosis increases cell number without changing specificity.