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.? nswer 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?

Answer : Step 1 of 4 : Given, As of April 2006, roughly 50 million .com web domain names were registered a) The claim is to find many domain names consisting of just two letters in sequence can be formed And How many domain names of length two are there if digits as well as letters are permitted as characters. There are 26 letters in alphabet. There are 26 possible ways to choose the first character and 26 possible ways to choose second Therefore, the possible number of domains with two letters is n n = 26 2 = 676 We have 10 digits and 26 alphabets So, totally 36 There are 36 possible ways to choose the first character as digits as well as letters and 36 possible ways to choose the second character as digits as well as letters. 2 therefore , n = 36 = 1296 Step 2 of 4 : b) The claim is to find many domain names consisting of three letters in sequence can be formed And How many of this length are there if either letters or digits are permitted There are 26 possible ways to choose the first character, 26 possible ways to choose second and 26 possible ways to choose third character. Therefore, the possible number of domains with three letters is n n = 26 3 = 17576 There are 36 possible ways to choose the first character as digits as well as letters, 36 possible ways to choose the second character as digits as well as letters and 36 possible ways to choose the third character as digits as well as letters. therefore , n = 363 = 46656