User

Students attending a certain university can select from $120$ 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. If any two$-$ or three$-$letter code is available to identify majors or double majors, how many major codes are available?