the number of ways in which the numbers 1,2,3,4,5,6,7 can be inserted in an empty Binary search tree is such that the resulting tree has a height 6, is ____? Note: the height of a tree w/ a single node is 0"

the answer is 2^6 = 64.

the reasoning is: "

For height 6, we have 2 choices. Either we select the root as 1 or 7. Suppose we select 7. Now, we have 6 nodes and remaining height = 5. So, now we have 2 ways to select root for this sub-tree also. Now, we keep on repeating the same procedure till remaining height = 1 For this last case also, we have 2 ways. Therefore, total number of ways = 2^6= 64"

my problem is: this is how i understand it: 1 or 7 is chosen as a root and all others are added after it making a structure tht looks like a straight line, because the height must be 6. but from my understanding, this would not give choice. so i don't understand how there is a choice of two after the root?