How old is nature girl? She doesn't know factorials, so... Some twelve years old or less? I guess most countries go over that by that age.
Factorials are a weird thing. I think you either learn them early, or not at all. I learned them, but have no idea what they are used for. It's possible it went into something in calculus or differential equations that I've forgotten over the years.
They're use in probability a lot. For example, if you have 10 people, and you have to place then in some order, there are 10 possible people who could be first, but then you only have 9 people to pick from for second place, then 8 possible people for third place, and so on, so the number of ways to order N-things is N-factorial.
If you're only selecting a subset, say you're selecting 3 things out of 10, then the possible choices are 10*9*8, which can be written as 10!/7! or N!/(N-X)!, where N is how many things you have and X is how many things you're selecting.
But the above formula treats different orderings as unique. if you don't care about the order, then you can consider the number of ways that
the three things you pulled out of the bag can be ordered, and that's just 3! from the above explanation. So you can divide your 10*9*8 value by 3*2*1 to collapse alternate orderings.
So the formula for number of possible triplets (unordered) that can be selected from a bag of 10 things should be 10!/7!/3!, and the general formula is N!/( (N-K)! * K! ) for the number of possible selections of K things you can pull out of a bag of N things.