Formula to count unique strings broken down by month

[Cabs1]

Hello all,

I have been struggling with this for a while so joined the forum so I can ask the experts .

I am trying to count the number of unique entries in a column (a) broken down by month (column c).
The data in column a is alphanumeric so I have been unable to use frequency.
I have attached an example which should hopefully make things clearer. I have highlighted the cells where I need a solution and have added a table of expected results.

I have a formula which calculates the totals by month but it counts all entries and doesn't ignore repeated entries.

=IF(COUNTIF($C$2:$C$19,8)=0,"0",(COUNTIF($C$2:$C$19,8)))

Via a google search I found that you could use the following formula (as an array) to calculate the total unique entries but I am unable to adapt it to allow for the month variable;

{=SUMPRODUCT((A2:A19<>"")/COUNTIF(A2:A19,A2:A19&""))}

Any suggestions would be gratefully received.

Thanks