Question

The number of rooted trees (NR) for n taxa is ______

(a) NR = (2n− 3)!/2^n+2 (n− 2)!

(b) NR = (2n− 3)!/2^n (n− 2)!

(c) NR = (2n− 3)!/2^n−2 (n− 5)!

(d) NR = (2n− 3)!/2^n−2 (n− 2)!

I have been asked this question in an internship interview.

Origin of the question is Forms of Tree Representation in division Molecular Phylogenetics of Bioinformatics

Answer 1

Correct answer is (d) NR = (2n− 3)!/2^n−2 (n− 2)!

The explanation: The number of potential tree topologies can be enormously large even with a moderate number of taxa. The increase of possible tree topologies follows an exponential function. In this formula, (2n−3)! Is a mathematical expression of factorial, which is the product of positive integers from 1 to 2n − 3. For example, 5! = 1 × 2 × 3 × 4 × 5 = 120.