As of April 2006, roughly 50 million .com web domain names were registered (e.g.

Question

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? 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? 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?

Explanation / Answer

a) number of sequence of 2 letters = 26*26 = 676

if digits as well as letters are allowed ,then for 1 position ,number of options = 26+10 = 36

hence total number of ways = 36*36 = 1296

b)similarly for 3 letters in sequence

number of ways = 26^3 = 17576

if digits are also permitted ,

then number of ways = 36^3 = 46656

c) 4-characters

26^4 = 456976

digits are include ,then 36^4 = 1679616

d)97786 of 4-letters are not claimed , then number of sequence which is owned = 36^4 - 97786

hence required probability= (36^4 - 97786)/36^4 = 0.94178074

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