This is not a good general interview level question, its premise is entirely based on a specific formula in graph theory without stating what it is. This type of question just tests if you know/remember a certain topic and can translate it to code. Not to mention the explanations are low quality in that it tells you to just imagine a tree using undefined terms like path and star instead of just providing a graphic? It tells you you're wrong for thinking its permutations, instead just think of a tree like you're supposed to already know Cayley's Formula and Kirchoff's theorem but if you did know it then the hint is circular and useless because then you wouldn't be trying to solve it using permutations. The writing of this challenge isn't even near the tier of previous ones that actually provide Wikipedia sources and graphics of what topics are being tested here.