The governing board of a district maintaining one or more secondary schools may, subject to such rules and regulations as may be prescribed by the State Board of Education and upon the authorization of the Superintendent of Public Instruction, provide pupils enrolled in the regular day schools of the district with instruction by correspondence provided by the University of California, or other university or college in California accredited for teacher training under this code, in subjects included within or related to the course of study offered in the school and which for good reason cannot be taken by the pupil, and pay the cost thereof. Such instruction when provided for a pupil must be a part of the program of study approved for such pupil.