Being able to count stuff is really important in game design. There are so many applications for combinatorics in video game design that it’s good to simply be aware that there is a science of counting!
You’ll see it in card games all the time. Say you have a deck of 40 unique cards and you draw a hand of 5 cards from that deck, how many unique hands of 5 could you possibly draw?
You can google the answer by typing “forty choose five” and the answer is 658,008
How many unique teams of six different Pokémon can you make from a choice of 151 types? Google “151 choose 6” and you’ll see that the number is very very big.
There are many more ways to count things. If your players visit six dungeons in any order, how many unique sequences of dungeons are there? (Try googling “6 factorial”)
Whenever you’re asking the question “how many possible ways?”, you’re dealing with combinatorics!