Thirty Two Bad Orders

You insert the keys 11 through 66 into an empty binary search tree, one at a time, with no rebalancing. There are 6!=7206! = 720 possible insertion orders. Some of them produce a tree of height 5, that is, a single path with no node having two children.

How many of the 720 orders produce such a path?

A

120

B

2

C

32

D

64