There are 24 4 possible orderings of four keys but only 14, Ask an Expert

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There are 24 = 4! possible orderings of four keys, but only 14 distinct binary trees with four nodes. Therefore these binary trees are not equally likely to occur as search trees. Find which one of the 14 binary search trees corresponds to each of the 24 possible orders. Thereby find the probability for building each of the binary search trees from randomly ordered input.

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