Applying Probability Theory to Alphabetical Ordering

The ordering of objects is one of the central topics of probability. Through the use of probability theory, I attempt to define a formula for a specific method of putting a list of names in alphabetical order. Beginning with the basic question of the probability that the first r in a list of n names are in alphabetical order, I then extend this question to ordering a list of names without any insertions . For example, if the name being considered comes before the first in the ordered list, it is placed on the top. If it comes after the last in the ordered list, it is placed on the bottom. Otherwise the name must be inserted somewhere in the middle of the list to put it into its proper place. I attempt to determine the probability that the first r names in a list of n can be put into alphabetical order without any insertions