Where are white blood cells produced?

Blood is produced in the bone marrow, a tissue in the central cavity inside almost all of the bones in the body. In infants, the marrow in most of the bones is actively involved in blood cell formation. By later adult life, active blood cell formation gradually ceases in the bones of the arms and legs and concentrates in the skull, spine, ribs, and pelvis.
White blood cells, Red blood cells and platelets grow from a single precursor cell, known as a hematopoietic stem cell. Remarkably, experiments have suggested that as few as 10 stem cells can, in four weeks, multiply into 30 trillion red blood cells, 30 billion white blood cells, and 1.2 trillion platelets—enough to replace every blood cell in the body.
The majority of white blood cells have a relatively short life span. They may survive only 18 to 36 hours after being released from the marrow. However, some of the white blood cells are responsible for maintaining what is called immunologic memory. These memory cells retain knowledge of what infectious organisms the body has previously been exposed to. If one of those organisms returns, the memory cells initiate an extremely rapid response designed to kill the foreign invader. Memory cells may live for years or even decades before dying.

Memory cells make immunizations possible. An immunization, also called a vaccination or an inoculation, is a method of using a vaccine to make the human body immune to certain diseases. A vaccine consists of an infectious agent that has been weakened or killed in the laboratory so that it cannot produce disease when injected into a person, but can spark the immune system to generate memory cells and antibodies specific for the infectious agent. If the infectious agent should ever invade that vaccinated person in the future, these memory cells will direct the cells of the immune system to target the invader before it has the opportunity to cause harm.
Platelets have a life span of seven to ten days in the blood. They either participate in clot formation during that time or, when they have reached the end of their lifetime, are eliminated by the spleen and, to a lesser extent, by the liver.