The number of structurally different possible binary trees with 4 nodes is
2017
The number of structurally different possible binary trees with 4 nodes is
- A.
14
- B.
12
- C.
336
- D.
168
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Correct answer: A
The number of structurally different binary trees with n nodes is determined by the nth Catalan number. The formula for the nth Catalan number is C_n = (1 / (n + 1)) * binomial(2n, n). For n = 4, this is (1 / 5) * binomial(8, 4). Calculating the combination: binomial(8, 4) = (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1) = 70. Therefore, the result is 70 / 5 = 14.
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