Question

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 STA, and math majors are 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 double major?

D) Are there enough major codes available to identify all single and double majors at University of Florida?

Answer 1

Answer:

1. 8385 double majors

2. 18252 major codes

3. 8515 codes

4. Yes

Step-by-step explanation:

Given

Major areas = 130

Alphabets = 26

a.

There are 130 major areas in the university.

To get a double majors, means one select any of two of the major areas in the university.

i.e. just 2 alphabets are needed

Number of Double Majors = 130C2

130C2 = 130!/(128!*2!)

130C2 = 130 * 129/2

130C2 = 8385.

b.

Number of major codes available = Number of 2 digit codes + Number of 3 digit codes

Number of 2 digit codes = 2 alphabets

There are 26 ways of selecting the first letter

There are 26 ways of selecting the second letter

So, number of 2 digit codes = 26 * 26 = 676.

Number of 3 digit codes = 3 alphabets

There are 26 ways of selecting the first letter

There are 26 ways of selecting the second letter

There are 26 ways of selecting the third letter

So, number of 3 digit codes = 26 * 26 * 26 = 17576

Thus, number of major codes = 17576 + 676 = 18252

c.

Number of codes to identify a student with either a single major or double major

Number off single major codes = number of major areas = 130

Number of double major codes = 8385

Total = 130 + 8385 = 8515

d. From the solutions above, Yes there are enough codes available to identify all single and double majors at the university