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GATE 2021 BT – Question 13

Recombinant DNA Technology and Other Tools in Biotechnology · Computational tools: Bioinformatics resources, databases, sequence analysis, alignment and phylogeny · 1 mark · Multiple choice

Number of unrooted trees in a phylogeny of five sequences is

  1. 3
  2. 15
  3. 105
  4. 945

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Correct answer: (B) 15

Explanation

The number of **unrooted binary trees** for $n$ sequences is
$$(2n-5)!!=(2n-5)(2n-7)\cdots3\cdot1 .$$

For $n=5$:
$$(2\cdot5-5)!!=5!!=5\times3\times1=\mathbf{15}.$$

(Check with smaller cases: $n=3$ gives 1 tree, $n=4$ gives 3 trees, $n=5$ gives 15 trees. The number of rooted trees is $(2n-3)!!=105$ for $n=5$, which is option C and is a different quantity.)