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Question related to distinct count

Below is very small sample of my data set.

I know that I can use distinct count to display total client count of 3.

What I'm trying to accomplish is creating a set analysis that is able to count distinct clients based on where the minimum date matches the entry date. With some help within qlik community, I was able to create a column identifier to show which row is client's first entry in the data set. 

All our outcome counts are based on client's first or last entry (service). A client may go in and out of program 20 times within a time period. My goal is to create a set analysis that counts first entry (Min) and then add an identifier to count specific outcomes.

Count({<IsCurrent={$(=If([Entry Date]=Min(total[Entry Date])))}>}Distinct[Client Id]),

For example, I'm trying to show a total count of 3 for streets.    


Client IdEntry Exit Provider NameEntry DateExit Date AdjustedMin Entry
758LSS - FM Faith on 6th3/22/20184/5/2018YesStreet
758LSS - FM Faith on 6th4/7/20184/12/2018NoRefused
758LSS - FM Faith on 6th4/26/20186/4/2018NoRental
2134LSS - FM Faith on 6th3/30/20186/15/2018YesStreet
2517LSS - FM Faith on 6th3/9/20185/9/2018YesStreet