Count how many rows contain a number of matches with another

I have this range C1:Q2000, each row contains 15 numeric values, and AA1:AT1 with 20 numeric values.
I need to count how many rows in C1:Q2000 contain 15 matches with AA1:AT1

This is the formula I use to count matches
=SUMPRODUCT(COUNTIF(C1:Q1, AA1:AT1))
But would only count one row at a time and I don't seem to come up with an idea of how to sum the counts of all the 2000 rows and only if there are 15 matching values.

All I know is I could make a column with the count of each row, and count how many times the result was 15, that would do it, but I have to repeat this from AA1:AT1 until AA3000:AT3000 and not only look for 15 matches but also 0,1,2... matches up to 15. It gets complicated... I'm looking if there is a simpler way.

I have found some sheets that do this with a smaller amount of numbers, but all use vba. Is there a way of doing this only using formulas?

Thanks for your help!

Hi, thanks.

I didn't know that was relevant as I don't have a fixed location in the world :P
but if it's necessary alright.
If that's for the language, I must tell I'm using excel in english and I only know the functions in english.

I'm uploading a reduced version with only a few rows so you can have an idea of what I'm working with, in this sample I just need to know how to count how many rows at C1:Q3 have 15 matching numbers with AA2:AT2 so I can do the rest.

This worked perfectly! Thank you