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
