Each person makes more than 1 million different b cell antigen receptors and more than 10 million different t cell antigen receptors. how is such diversity in antigen receptors generated?

This is due to a phenomenon referred to as somatic hypermutation. The variable regions of the b and t cell receptors, including the variable region of the immunoglobulins, undergo rapid changes due to rapid mutations in the genetic material that codes them. This allows them to adapt quickly to novel invaders. This phenomenon is then followed by affinity maturation when the effective receptors and Igs are preserved