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ISRO-DEC2017-28

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5 votes
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The number of structurally different possible binary trees with $4$ nodes is 

  1. $14$
  2. $12$
  3. $336$
  4. $168$
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  • structurally different  trees = Unlabeled trees 
  • Number of Unlabeled binary trees = (2n)!/(n+1)!n!  [Catalan Number]
    • Here n =4
    • answer = 8!/(5! 4!) =14
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No of unlabelled binary trees on n nodes = $\frac{_{n}^{2n}\textrm{C}}{n+1}$

No of labelled binary trees on n nodes = $\left ( \frac{_{n}^{2n}\textrm{C}}{n+1} \right )*n!$

Structurally different = unlabelled = $\frac{_{4}^{8}\textrm{C}}{5}$ = $14$
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