Question related to distinct count

[jbakerstull]

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 Id	Entry Exit Provider Name	Entry Date	Exit Date Adjusted	Min	Entry
758	LSS - FM Faith on 6th	3/22/2018	4/5/2018	Yes	Street
758	LSS - FM Faith on 6th	4/7/2018	4/12/2018	No	Refused
758	LSS - FM Faith on 6th	4/26/2018	6/4/2018	No	Rental
2134	LSS - FM Faith on 6th	3/30/2018	6/15/2018	Yes	Street
2517	LSS - FM Faith on 6th	3/9/2018	5/9/2018	Yes	Street