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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» 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.


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