Suppose that a local area network requires seven letters for user names. lower - and uppercase letters are considered the same. how many user names are possible for the local area network?

If a user name can have seven letters (with no distinction between upper and lower case), and if a letter can be repeated, then the maximum number of names is 26x26x26x26x26x26x26, or 8,031,810,176. That is, slightly more than eight billion names are possible.