@professionalbronco Yeah that's exactly right! Great job for coming up with that, it's a really crucial concept for counting problems.
Actually, if you notice, towards the end of that video in Part 5 Prof. Loh does something very similar, he divides by 2 to account for each "pair" since only one arrangement in each fulfills the conditions. It's basically what you were thinking of but kinda the reverse! Great minds think alike