Final answer:
The question deals with combinations, which involve selecting a set number from a larger group where order does not matter. The student must find the combination of 5 courses that corresponds to one of the provided set numbers by using the combination formula C(n, k) = n! / [k! * (n - k)!]. The result will determine the total number of courses available for selection.
Step-by-step explanation:
The question posted by the student pertains to the concept of combinations, specifically in the context of selecting a number of courses from a larger list. When asking about different sets of five courses from a given number, the mathematical operation involved is a combination where order does not matter. Therefore, to find how many different sets of five courses are possible, we use the combination formula:
C(n, k) = n! / [k! * (n - k)!]
where n is the total number of courses to choose from, k is the number of courses to be chosen, n! represents the factorial of n, and k! is the factorial of k.
The number of possible outcomes (or microstates) should match one of the given numbers, such as 80, 720, 840 or 480, which represent different combinations of choosing 5 courses.
We are not given the total number of courses here, but we know that:
C(n, 5) = n! / [5! * (n - 5)!]
The student should match this expression with one of the options (a, b, c or d) to get the number of total courses (n).