Counting cells with numbers in the column that contains specific words

Hi all,

I’m trying to build a function, but I haven’t been able to successfully navigate some of the eccentricities of Excel formula-building.

Right now I am working on counting all of the cells that contain numbers (so likely just a =COUNT function), but will be eventually getting other descriptive stats as well. My problem is that I would like to create a formula that will perform the counting/mean calculation, etc., but only on a specific column that has the header cell that contains several specific words. Rather than having to type in the target words for each column, I would like to have the target words in the function be imported from multiple designated cells.

For example,

I want to find how many numbered cells are found in column E headed as "dog brown,” but I also have columns headed as "cat brown" "dog black" etc. (which I will be using the formula on later)
to paint a small picture, in my descriptives table, "dog" is in B31 and “brown” is in C30, then “cat” in B32 and “black” in D30.


UPDATE: people are smart and helpful and I have no more worries in this world
Solved by the lovely internet people.xlsx