How many different ways can you go about completing a course/ class at university?

Question

How many different combinations of results in assignments are possible in a University course?

I am interesting in calculating the number of unique ways I can finish this course that I am doing. To make things easier, there are no partial marks.

Here are some conditions:

• There are four assessable tasks

  • Assignment 1: Weighted 10%
  • Assignment 2: Weighted 15%
  • Assignment 3: Weighted 15%
  • Assignment 4: Weighted 60%

• Possible marks for each assessment:

  • Assignment 1: /10
  • Assignment 2: /10
  • Assignment 3: /10
  • Assignment 4: /100

I am a little rusty on my combinations discrete mathematics. Can this be viewed as a pigeonhole principle problem or would this be permutations/combinatrix?

From an algorithmic point of view, how would you go about solving this?

TL/DR: How many combinations of indiviudal graded assessments can you get in a course? What is the range of end of semester marks possible?

Thank you for your time.

Answer 1

Eureka

By writing a small block of code I was able to find out 134431 unique combinations of grades!! This surpised me, mostly because I don't understand entirely why this is the case.

I am still curious as to how you would solve this mathematically instead of programmatically... don't hesitate to correct me or prove otherwise either !!

thank you everyone :)