Count based on rows and columns

I have a data table with two columns (surveillance #, date). I would like to count the number of times a particular surveillance # occured during a particular month, without doing a pivot table. In the attached example cell E2 i have the following equation

=LOOKUP(2,1/(($D2=$A$2:$A$50)*(MONTH(E$1)=MONTH($B$2:$B$50))*(YEAR(E$1)=YEAR($B$2:$B$50))))

which results in a value of 1, but not a count of the number of times surveillance #1 occurs in the month of January. Can someone point me in the right direction for how to make this return a count?

Any help is appreciated.

Thanks!