Search for 2 values, 1st one then the other both must match, and return a total count.

Hello and Thank you for entertaining my question/problem.

I am trying to write a formula in a cell, that reads a range of data in one column, then read data in each row, and if it finds two matching specified values, it will look at count each occurrences, and return with a total count in a separate cell. So below is the sample data, and A7 is where I want the information, which is =X:

Range 1: A1:A4
Range 2: each corresponding row
Search for Value in Range 1: "AB"
Search for Value in Range 2: "400"
If search in Range 1 is a match, then search in that row in Column B, if that row matches Range 2 value, count 1 for each occurrence.
Returned Result in A7: 2

A B
1 Noun Number
2 AB 400 <--Match
3 AB 100
4 SRA 400
5 SRA 200
6 AB 400 <-- Match
7 2

Thank you again. I'm thinking I might have to brush up on some VBA, but I like to avoid it, if possible.

(I am working with Excel 2012, which the expectation of upgrading to 2016 (at work). However, I use Office 365 on the go and 2016 at home.)

Yes! Countifs (Forgot about ifs.) Thank you Ron! Much appreciated!