Hi @victorioussheep ! It's true that "number of subsets of a set of size 3" might be a bit of a mouthful compared to just "2^3". That's one of the nice things about math-- it simplifies sometimes confusing words into easier expressions! But in the video's case, the "number of subsets of a set of size 3" comes from what we want to find: we want to know the number of topping choices where we have at least one of (ketchup, mustard, lettuce) on the burger. So the "set of size 3" is the set (ketchup, mustard, lettuce), and the "subset" is a particular topping choice from there. We are counting up how many subsets there are. And that amount equals 2^3, as Prof. Loh explained in the video.
So although the first expression is a bit long and maybe convoluted, it's helpful since it clarifies what exactly we're trying to solve, and 2^3 is the answer to that question. If the first wordy expression comes intuitively to you, though, at that point you can skip over it!
@professionalbronco Yes, that definitely works! It's interesting how both strategies are useful in different cases- Prof. Loh's method is faster when considering larger numbers, but yours is quicker in this case with smaller numbers Nice!
In the question it says that Alicia has to be first in line, so there are \(3!=6\) ways, which is equal to the ways they can be arranged in a circle. The question only asks you if the answers are the same.