Question

As of April 2006, roughly 50 million .com web domain names were registered (e.g. ya-hoo.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 per-mitted as characters?i. 262=676ii. 362=1,296

b.How many domain names are there consisting of three letters in sequence? How manyof this length are there if either letters or digits are permitted?i. 263=17,576ii. 363=46,656

c.Answer the question posed in (b) for four-character sequences.i. 264=456,976ii. 364=1,679,616
d.As of April 2006, 97,786 of the four-character sequences using either letters or digitshad not yet been claimed. If a four-character name is randomly selected, what is theprobability that it is already owned?

Answer 1

Answer:a) Two letter name =676

Three letter name with digits and letters= 1296

b) Domain names with 3 letters=17576

c)4 character letters=1679616

Probability of picking an occupied 4 character name = 0.0582

Explanation:

a) There are 26 letters in the English alphabet. Combining 2 domain names with letters alone will be 26^2= 26×26=676

If digits are allowed with letters: There are 10 digits from 0-9.

Therefore 26 letters + 10 digits = 36

36^2=36×37= 1296

If neither letters nor digits are allowed,it is = 0

b)Three domain name = 36^3=36×36×36=46656

c)4 character domain names with letters and digits =36^4=36×36×36×36= 1679616

d) Probability of picking 4 character domain name = 97786/1679616 = 0.0582