multiple criteria to select number

I have one data set COUNTIFS(A1:D10, Berwick)

If Berwick appears it would be classed as 1

In a the same formula set, I would like to count : E1:F10

when "Berwick" and "Clinic visit" appear 

if these two appear it will be classed as 1

if they appear in the data set twice it would be counted as 2

So in the one formula:

A1:D110, Berwick

E1:f10 Berwick, Clinic visit

Example

column data A1:d10

Berwick is listed 3 times

column data E1:f10

Berwick (E:2), Clinic visit  (F:5)  (different cells) is listed 2 times

The formula = 5