How many unrooted trees are possible for a six-species tree and a seven-species tree,respectively?
A)6 and 7
B)15 and 25
C)105 and 945
D)More than there are stars in the universe

Question

Quizplus · Accepted Answer

The number of unrooted trees can be computed using Cayley's formula, which states that there are (n-2)! possible unrooted trees for a tree of n nodes. 
For a six-species tree, there are (6-2)! = 4! = 24 possible unrooted trees. 
For a seven-species tree, there are (7-2)! = 5! = 120 possible unrooted trees. 
Therefore, the answer is C) 105 and 945.

How Many Unrooted Trees Are Possible for a Six-Species Tree