**Question**: what is the number of trees T(V,E) on the set $({v\_1,v\_2,v\_3,v\_4,v\_5,v\_6,v\_7,v\_8})$ that have at least **two** vertices with a 3 degree.

edit: would like if someone can confirm I did it right: 

total number of trees: $8^6 - \frac{8!}{2} - \frac{6!}{2} \* 8 \* 7 = 221824 $

Thanks in advance!