Question

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. What is the maximum number of possible double majors available to University of Florida students?

Answer 1

7,140

Explanation:

Given the following :

Total Number of majors = 120

To obtain a double major, any to majors are combined) 2

Hence, maximum number of double majors available by obtaining 120C2.

Recall :

nCr = n! / (n-r)! r!

120C2 = 120!/(120-2)!2!

120! / 118! × 2!

= (120 × 119) / 2 * 1

= 14280 / 2

= 7140 ways.

Hence, there are a maximum of 7,140 ways of combining two majors