Question

Number of unrooted trees in a phylogeny of five sequences is

• A. 3
• B. 15
• C. 105
• D. 945

Hint:

Unrooted tree formula: (2n − 5)!!. Multiply descending odd numbers to 1.

Answer 1

The Correct Option is B

The number of unrooted phylogenetic trees for \( n \) taxa is given by the formula:
\[ (2n - 5)!!
\] For \( n = 5 \):
\[ (2 \times 5 - 5)!! = 5!!
\] Double factorial of 5 means multiplying all odd integers down to 1:
\[ 5!! = 5 \times 3 \times 1 = 15
\] Thus, there are exactly 15 possible unrooted trees for five sequences.
Options 3 and 105 correspond to smaller or larger taxa counts, and 945 is for even larger sets.
Therefore, option (B) is correct.