Trying to count how many columns contain a phrase in any row where another phrase is present

I have a sheet recording attendance at meetings where there are delegates from different companies. I want to be able to count how many times a specific company has had a delegate present.

similar sheet using example data

In the pictured example, you can see that Googie's only delegate was present at 4 meetings, which would be easy to count:

=COUNTIF(C12:I12,"present")

Coopers had at least 1 delegate at 6 meetings.

I can get a total number of cells with "present" in them where column B has "Coopers" in it:

=SUMPRODUCT((B2:B14="Coopers") * ISNUMBER(SEARCH("present",(C2:I14)))

How can I get it to filter only rows with "Coopers" in them and count how many columns (not cells) contain the word "present"?

I'm using Microsoft Excel for Microsoft 365 MSO