The answer is 1.

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In a BST, all elements in any left sub-tree must be smaller than the root, and all elements in any right sub-tree must be larger.

Since there are 3 elements in the left and right trees, this means that 4 has to be the root of the tree. In the left sub-tree, using a similar argument, 2 has to be the root with 1 and 3 as the leaves. On the right sub-tree, 6 has to be the root, with 5 and 7 as the leaves. This gives only 1 valid BST.