Suppose that a local area network requires ten letters for user names. Lower- and uppercase letters are considered the same.

Homework Help: Questions and Answers: Suppose that a local area network requires ten letters for user names. Lower- and uppercase letters are considered the same. How many user names are possible for the local area network?

How many user names are possible for the local area network?
A. 26¹⁰
B. 10
C. 10 !
D. 26

Answer

To solve this problem, let’s understand the Requirements

• Length of user name: 10 letters.
• Uppercase and lowercase are considered the same: This means we only have 26 unique letters (A-Z) available.

Determine the Total Number of Combinations

Since each letter of the user name can be one of 26 letters, and the user name is 10 letters long, we need to determine the number of possible combinations of letters for each position in the user name.

Calculate the Number of Combinations

• For the first letter, there are 26 choices.
• For the second letter, there are also 26 choices.
• This continues for all 10 letters.

The total number of possible user names can be calculated as: 26¹⁰

Given Option: Step by Step Answering

a) 26¹⁰

• This is the correct answer because as it represents the number of ways to choose each of the 10 letters from 26 possibilities.

B. 10

• This is incorrect, as it doesn’t represent the total number of combinations.

C. 10!

• This is the number of ways to arrange 10 items, which is unrelated to the combination of letters here.

D. 26

• This is the number of letters available, but it doesn’t account for the 10-letter length of each user name.

Final Answer

Based on the above analysis, the correct answer is:

a) 26¹⁰

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