Discussion
Number of binary trees formed with 5 nodes are
Answer: D
The number of different binary trees that can be formed with n nodes is the Catalan number, the binomial coefficient of 2n over n divided by n + 1. For n = 5 this is
\[ \frac{1}{6}\binom{10}{5} = \frac{252}{6} = 42 \]
So there are 42 binary trees with 5 nodes, option (D). The values 32 and 120 are 2 to the power 5 and 5 factorial, which do not count binary tree shapes, and 36 is not the Catalan number.
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