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As of April 2006, roughly 50 million web domain names were registered (e.g., ). 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.] ANSWER ↓ 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.] ANSWER ↓ Answer the questions posed in (b) for four-character sequences. ANSWER ↓

Respuesta :

nuhulawal20

Answer:

a) 676, 1296

b) 17576, 46656

c) 456976, 1679616

Step-by-step explanation:

firstly we know that there are 26 letters in the alphabet.

there are 26 ways of choosing the first character and 26 ways choosing the second character,

Therefore, the possible number of domains with two leeter is;

n = 26²

= 26 × 26

= 676

now when the digits are allowed, there are 26 + 10 = 36 characters to be used in total

therefore the possible number of domains with two characters is;

n = 36²

= 36 × 36

= 1296

b)

there are 26 ways of choosing each character

therefore, the possible number of domains with three letters is

n = 26³

= 26 × 26 × 26

= 17576

when the digits are allowed, there are 26 + 10 = 36 characters to be used in total

therefore , the possible number of domains with three characters is;

n = 36³

= 36 × 36 × 36

= 46656

c)

there are 26 ways of choosing each character, therefore the possible number of domains with four letters is;

n = 26⁴

n = 26 × 26 × 26 × 26

n = 456976

when the digits are allowed, there are 26 + 10 = 36 characters to be used in total

therefore, the possible number of domains with four characters is;

n = 36⁴

n = 36 × 36 × 36 × 36

= 1679616

There are 676 domain names consisting of just two letters in a sequence that can be formed.

There are 1296 domain names of length two are there if digits, as well as letters, are per-mitted as characters.

There are 17576 domain names are there consisting of three letters in sequence.

There are 46656 of this length are there if either letters or digits are permitted.

Given

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

1. How many domain names consisting of just two letters in sequence can be formed?

There are 26 letters in the English alphabet.

Combining 2 domain names with letters alone will be;

[tex]\rm =n^2\\\\ = 26^2\\\\ =26 \times 26\\\\=676[/tex]

2. How many domain names of length two are there if digits, as well as letters, are per-mitted as characters.

If digits are allowed with letters:

There are 10 digits from 0-9.

Therefore 26 letters + 10 digits = 36

[tex]\rm = n^2 \\\\= 36^2 \\\\ = 36 \times 36 \\\\ = 1296[/tex]

3. How many domain names are there consisting of three letters in sequence?

There are 26 ways of choosing each character;

Therefore, the possible number of domains with three letters is;

[tex]= \rm n^3\\\\= 26^3\\\\= 26 \times 26 \times 26\\\\= 17576[/tex]

4. How many of this length are there if either letters or digits are permitted?

The digits are allowed, there are 26 + 10 = 36 characters to be used in total

Therefore, the possible number of domains with three characters is;

[tex]\rm = n^3 \\\\= 36^3 \\\\ = 36 \times 36 \times 36\\\\ = 46656[/tex]

To know more about Digits click the link given below.

https://brainly.com/question/1291874

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