Distinct or group by on some columns but not others

I have a view that I'm trying to filter with something similar to DISTINCT on some columns but not others.

I have a view like this:

Name
LastName
Zip
Street1
HouseholdID (may not be unique because it may have multiple addresses -- think of it in the logical sense as grouping persons but not physical locations; If you lookup HouseholdID 4130, you may get two rows.. or more, because the person may have mutiple mailing locations)
City
State

I need to pull all those columns but filter on LastName,Zip, and Street1. Here's the fun part: The filter is arbitrary -- meaning I don't care which one of the duplicates goes away. This is for a mail out type thing and the other information is not used for any other reason than than to look up a specific person if needed (I have no idea why). So.. given one of the records, you can easily figure o开发者_开发知识库ut the removed ones.

As it stands now, my Sql-Fu fails me and I'm filtering in C# which is incredibly slow and is pretty much a foreach that starts with an empty list and adds the row in if the combined last name, zip, and street aren't are not in the list.

I feel like I'm missing a simple / basic part of SQL that I should be understanding.

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Solution can be assuming we have Unique Identification column in view:

Select Name,
       LastName,
       Zip,
       Street1,
       HouseholdID, 
       City,
       State

From View V1

INNER JOIN 
(
    Select Min([Unique Identification]) as ID
    From View v
    Group By LastName,
             Zip,
             Street ) AS T on T.ID = V1.[Unique Identification]

When No Identifier in View .......

Select     Name,
           LastName,
           Zip,
           Street1,
           HouseholdID, 
           City,
           State

    From  
    (
        Select Name,
               LastName,
               Zip,
               Street1,
               HouseholdID, 
               City,
               State,
               Row_Number() Over (Partition By LastName,Zip,Street Order By Street1,HouseholdID,City,State) AS RowNum
        From View v
        ) AS T 
Where T.RowNum = 1