The problem I am working on is:
As of April 2006, roughly 50 million .com web domain names were registered (e.g., yahoo.com).
a. How many domain names consisting of just two letters in sequence can be formed? How many domain names of length two are there if digits as well as letters are permitted as characters? [Note:A character length of three or more is now mandated.]
b. How many domain names are there consisting of three letters in sequence? How many of this length are there if either letters or digits are permitted? [Note:All are currently taken.]
c. Answer the questions posed in (b) for four-character sequences.
d. As of April 2006, 97,786 of the four-character sequences using either letters or digits had not yet been claimed. If a four-character name is randomly selected, what is the probability that it is already owned?
What I was wondering was, say that I wanted to know the number of domains where lexicographic ordering was of concern; that is, if b was the first letter in the domain name, then a couldn't be the next one, only letters that follow b. Would I count in this manner, $25\cdot24+24\cdot23+23\cdot22+22\cdot21+...3\cdot2+2\cdot1=5152$? I'm sure there is alternate way, too. Would it involve me finding the total number of domains, both in lexicographic order and not in lexicographic order, and subtracting something from that, right? Would $26^3=17576$ be the total number of combinations?