Suppose that a local area network requires eight letters for user names. Lower - and uppercase letters are considered the same. How many user names are possible for the local area network?

208,827,064,576 user names

Step-by-step explanation:

There are "8" places for each letter of the alphabet.

Since upper and lowercase are same and let's assume repetition is possible, we can say that each "placeholder" can hold 26 letters.

According to counting rule, we have to multiply the number of possibilities in each "place". That would be:

26*26*26*26*26*26*26*26 = 208,827,064,576 user names

There are over 208 billion user names possible (!)

Answer:62990928000 usernames

Step-by-step explanation:

Eight letters are required for username from a possible 26 alphabets

Upper and lower case are considered the same, so we have 26alphabets to choose from.

In combining the letters to form the username, the order of the letters are important.

In thus case, we use permutation

nPr = n! / (n-r) ! r!

n = 26, r = 8

26P8 = 26! / (18!) 8!

= 62990928000 usernames