(a)

Scenario: As of April 2006, roughly 50 million .com web domain names were registered.

Problem: 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?

Process: There are 26 letters in the English alphabet and 10 numerals.

Answer: 676 and 1,296.

(b)

Problem: 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?

Process: There are 26 letters in the English alphabet and 10 numerals.

Answer: 17,576 and 46,656.

(c)

Problem: How many domain names are there consisting of four letters in sequence? How many of this length are there if either letters or digits are permitted?

Process: There are 26 letters in the English alphabet and 10 numerals.

Answer: 456,976 and 1,679,616.

(d)

Problem: As of a certain date, 95,875 of the four-character sequences using either letters or digits had not yet been claimed. If a four-character name is randomly selected on that date, what is the probability that it is already owned?

Process: The probability of randomly picking a four-character domain name that has not yet been claimed is . The complement of this probability is the probability that a randomly picked four-character domain name is already owned.

Answer: 0.9429.