Following are the calculated fields and filters I have used based on the description you have provided.
Created a contains based condition to find if the words are present in product names. I am not good at regex but you can use regex_match in case of your conditions.
Since you have asked the counts of each product bought I have included product name as part of the calculation. If you wanted any of the 3 products, then product name can be removed from the calculation.
You can use the above filter.
Hope this helps. We can discuss on how it works if you are ok with the solution.