Filtering dynamically with slicer selections

Hello,

This is maybe a bit of a tricky one. I have a dataset which counts unique people aggregated by demographic and purchasing variables:

(e.g. 32 females aged 10-19 purchased Apples and Pears).

I'd like to create a slicer where users can select multiple values for the listed fruits (Apples, Oranges, Pears, Peaches and Kiwi), then count the total number of unique people (N) who purchase at least one of the selected fruits. (e.g. rows 1,4,5 and 6 all purchased apples and/or kiwis, so if a user selects Apples and Kiwis, I will sum(n) on all those rows). 

Most guides I've found have suggested unpivoting the data table, but if I do this it will cause aggregate groups that have more than one of the selected fruits to be duplicated in the rows, which will make my sums of [n] inaccurate. 

Some other work arounds I've considered or attempted are:

• Import the data unaggregated and unpivoted. I'd prefer to avoid this as the table will be tens of millions of rows, and is slightly less private/secure. 
• Dynamically write a sum if statement in dax which uses the slicer selections (from what I can tell, this isn't possible, particularly if the slicer is set as multiselect). 
• Create a calculated column which draws on a measure that concatonates the slicer selections and uses CONTAINSSTRING() to generate a flag I can use for filtering (I thought this worked, but it appears that the calculated column doesn't update dynamically when the slicer selections change). 

I'm at a loss what to attempt next, and hoping someone has a good idea!