The following binary tree has as many nodes as possible for a tree of height 5. Definition: A climb is a path that starts at the root and ends at a leaf. For example, the path indicated by the black lines is a climb. First, determine how many different climbs are in this tree. Then, suppose you have a list of 115 names, and you need to assign a name from this list to each climb. You may not repeat names. How many different ways are there to do this? There are --Select-- ways to assign the names to the climbs in this tree.