countif formula for multiple conditions in the same coloumn

Hi All,

I want to count the number of "a"s and "b"s in column 1 if the relevant column 2 value is equal to "aa" or "bb". please refer below data set. Answer should be 4.

Here is the formula i used for this,

=SUMPRODUCT(COUNTIFS(E16:E25,{"aa","bb"},C16:C25,OR("a","b")))

a - aa
d - aa
b - bb
b - aa
c - cc
b - dd
a - ee