antibodies

An Antibody is a large protein molecule which latches on to and neutralizes foreign invaders such as bacteria and viruses. Each antibody acts only on a very specific target molecule, known as an antigen. (It can also coat microbes in a way to make them palatable to scavenger cells such as microphages.) 

Mammals have an inherent capacity to synthesize billions of different antibodies. Exposure of the enormous repertoire of different antibodies to a foreign molecule is followed by the selection and growth of the cells bearing just those antibodies that fit the foreign chemical structure of a given antigen sufficiently well, even a structure that never occurred before in the history of the Earth. The arrival of an antigen only accelerates the formation of the antibody that makes the best fit. This Darwinian process of variation and selection is called the theory of clonal selection. 

If genes dictate the manufacture of antibodies, (through the information flow from DNA to RNA to proteins) how can a sufficient variety of antibodies be manufactured to deal with the variety of antigens that the body may encounter?