The number of different binary trees with 6 nodes is ______.
2016
The number of different binary trees with 6 nodes is ______.
- A.
6
- B.
42
- C.
132
- D.
256
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Correct answer: C
Answer: 132
Method:
Use the Catalan number formula for the number of different (rooted, ordered) binary trees with n nodes: C_n = 1/(n+1) * binom(2n, n).
Substitute n = 6 to get C_6 = 1/7 * binom(12, 6).
Compute the binomial coefficient: binom(12,6) = 924.
Divide by 7: 924 / 7 = 132, so the number of different binary trees with 6 nodes is 132.