New user account without applications from other accounts?

Hi. I'm trying to create a completely blank, fresh admin account on my Mac. I'm having some trouble, however, because the applications from the previous admin account are already there, in the new account. What am I doing wrong and is there some way to avoid this? Thanks.

Any applications that were installed into the default Applications folder at the root of the drive are going to be available in every account you create.
None of the preferences that were set in an one user account for those applications will be in the new account.
The preferences will all be back to the default, original install settings.

Only applications that were installed into a users Applications folder would not be available in a newly created account.