Question:

What is the maximum number of binary trees possible with 4 nodes?

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The Catalan numbers provide the maximum number of binary trees that can be formed with a given number of nodes.

Updated On: May 3, 2025

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The Correct Option is C

Solution and Explanation

The maximum number of binary trees possible with \( n \) nodes is given by the \( n \)-th Catalan number. For 4 nodes, the Catalan number \( C_4 \) is: \[ C_4 = \frac{1}{5} \times \left( \binom{8}{4} \right) = 14. \]
Thus, the maximum number of binary trees with 4 nodes is \( 14 \).

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