Here is an example of the type of problem I am trying to solve/optimize:
I have 12 classes I need/want to take. Let's say in the end I can only choose five. I want to see all the possible combinations of classes I can take (without having any time overlap). What is the most efficient way to do this?
I know how to compare two classes by making an Excel sheet like so (assume A, B, C... are abbreviations for classes, and N means the classes overlap/are at the same time while Y means they do not)
|O|A|B|C|D|E|...
|A|O|Y|N|Y|Y|...
|B|Y|O|Y|Y|Y|...
|C|N|Y|O|N|Y|...
|D|Y|Y|N|O|Y|...
|E|Y|Y|Y|Y|O|...
|...|
The problem with this is that it only lets me look at whether I can take two classes at the same time, which isn't super helpful because I need to take more than two classes.
Keep in mind I don't care about the number of combinations so much as seeing what they look like. I only care about the number if it means there are way too many combinations to look at.
Based on my calculations, I will end up having 12!/(12-5)! (or 12*11*10*9*8) possibilities, which is 95,040. Is this correct? Is there any other way to look at this?