SUMPRODUCT with COUNTIF to find unique entries

Attached is a simulation file using SUMPRODUCT AND COUNTIF.

Formula:

=ROUNDUP(SUMPRODUCT(--(B2:B16=F3)/COUNTIF(A2:A16,A2:A16)),0)

Customer ID : A2:A16
Entries Month : B2:B16
Lookup Month : F3

Problem
However if you look at the attached file, this formula does not return the correct answer.

Current Solution
I insert a new column (C) and to combine the text together.
E.g. C2 = A2&B2

Then I use the below formula,

Formula:

=SUMPRODUCT(--(B2:B16=F3)/COUNTIF(C2:C16,C2:C16))

I got the correct result, but...

Question
Is it possible to have one formula instead of inserting a new column?

I tried

Formula:

=SUMPRODUCT(--(B2:B16=F3)/COUNTIF(A2:A16&B2:B16,A2:A16&B2:B16))

Formula:

=SUMPRODUCT(--(B2:B16=F3)/COUNTIF(INDEX(A2:A16&B2:B16,0),INDEX(A2:A16&B2:B16,0)))

Formula:

=SUMPRODUCT(--(B2:B16=F3)/COUNTIF(SUMPRODUCT(--(A2:A16&B2:B16=A2:A16&F3)),SUMPRODUCT(--(A2:A16&B2:B16=A2:A16&F3))))

All failed...

Your advice would be greatly appreciated.