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When searching for the key value 50 in a binary search tree, node containing the key values 10, 30, 40, 70, 90, 120, 150, 175 are traversed, in any order. The number of different orders passing in which these keys values can occur on the search path from the root to node containing the value 50 are ________.
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$\frac{8!}{3!.5!} = 56.$


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