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CMI-2021-DataScience-A: 5

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A binary tree starts with a single root node at the top of the tree. Each node can have either a left child or a right child, or both, or neither. The children of a node are drawn below it, connected by edges. Here are the five possible binary trees with three nodes.

Note that the directions left and right of the children matter. In the second tree, the root has a left child that has a left child, while, in the fourth tree, the root has a left child that has a right child, and so on.

How many different binary trees can be constructed with four nodes?

  1. $13$
  2. $15$
  3. $14$
  4. $30$
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