This draft is a month old and I don’t remember where I was going with it. Good thing I have low standards.
I’ve been working my way through a discrete math course that I found at my library on DVD. I like the description the lecturer gives for the course: “It’s kindergarten math for grownups.”
One thing that comes up a lot in the combinatorics lectures is the quantity “N choose K”, usually written as .
It refers to the number of ways you can choose K things from a pool of N things, and you aren’t allowed to choose the same one twice. Maybe you’re at the end of Final Fantasy VII and you need to choose your 3 best characters to fight Sephiroth. If you have both optional characters, then you get to choose from Cloud, Tifa, Barret, Red XII, Cait Sith, Cid, Yuffie, and Vincent. That’s 3 characters from 8 candidates, or “8 choose 3”.
The number of ways to actually choose K things from N things turns out to be (n!)/(k!(n-k)!), which is kinda hard to write out a bunch of times. So most formulas just leave it as N choose K, or .