Problem 49E

Students attending the University of Florida can select from 130 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 University of Florida 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 of Florida?

Answer:

Step 1 of 4:

(a)

In this question, we are asked to find the maximum number of possible double majors available to the University of Florida students.

Students attending the University of Florida can select frommajor areas of study and the major is identified with a two-or-three-letter code. Some students opt for a double major. The Registrar was asked to consider assigning these double majors a different two-or-three letter code.

Lets denote the number of major areas of study available to the students of ta University of Florida to which is equal to

Since some students opt for a double major, then we can denote this with which will be equal to .

Here we can apply the combination theorem,

The number of unordered subsets of size chosen (without replacement) from available object is

……………..(1)

Substitute and into equation (1),

Hence the maximum number of possible double majors available to a University of Florida students is 8385.