I'm trying to figure out what is the flaw in my thinking for this practice question. If a tree has $10$ vertices, one of which must have degree of $8$, this means that we essentially have a $K_{1,8}$ star. So the extra vertex can go in one of 8 places, so wouldn't the number of such trees be $8$?
However, the answers provided says it says the answer is $8\cdot10\cdot9 = 720$ ??
What am I misunderstanding about this question?
Many thanks!