Students attending a certain university can select from 140 major areas of study. A student's major is identified in the registrar's records with a two-or three-letter code (for example, statistics majors are identified by STA, math majors by MS). Some students opt for a double major and complete the requirements for both of the major areas before graduation. The registrar was asked to consider assigning these double majors a distinct two- or three-letter code so that they could be identified through the student records system. (a) What is the maximum number of possible double majors available to the university's students?
(b) If any two- or three-letter code is available to identify majors or double majors, how many major codes are available?
(c) How many major codes are required to identify students who have either a single major or a double major?
(d) Are there enough major codes available to identify all single and double majors at the university?