Is this meandering off track just a wee bit?I'll participate. It'll be a fun thing to do. However, after thinking about it for about 30 seconds, it could get a little messy. Not all substitutions would be a "new" combination. Some substitutions will be a previous used combination. The easiest example: the original starting 5 coming out to start the second half. Counting just the unique combinations, and counting them just once, won't make the job any easier.
I've been in IT for about 50 years, starting in the days when mainframes roamed the earth, in a wide variety of roles. Great career for someone who studied physics and maths...
Living out here, a very few thousand kilometres from the ice wall surrounding our flat earth[1], we don't get much live coverage of our team's games. So I'm often listening to the audio stream from the Varsity Network while watching live stats from StatBroadcast.
Putting those together, it should be possible to develop a database[2] system to record the substitution log, so we'd know the on-court 5 at any time, to the minute. Analysis of the database would allow us to calculate the different combinations, how many time each had been used, and how long each combo had been on court.
The log only records substitution time to the minutes...
However, it might have to be real-time data acquisition. I've had a look at the archive of the BC game on the 14th (my time - 13th for the USAians) and only the last half dozen or so subs are recorded. This adds some complication as a screen scraper would have to be developed to capture subs as they happen.
Maybe someone has done something similar, as I'm sure I've seen charts showing who is one the floor in posts here. If someone can point me to a source for these I'll see if there's a way to do the combination analysis...
Feetnote:
[1] No correspondence shall be entered in to. Put this together with the subjects I studied in depth and work out for yourself if this is a joke - or not.
[2] This is the type of task that people often try to perform with a spreadsheet. A good way to tie yourself in knots!