Question:
What is the maximum number of binary trees possible with 4 nodes?
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
- 16
- 15
- 14
- 10
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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 \( 14 \).
Thus, the maximum number of binary trees with 4 nodes is \( 14 \).
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