Hope you can help!!

Column A=dates eg 17/06/05 etc
Column B=Product eg A, B, C, D, E etc
Column C=Quantity eg 1, 2, 3, 4, 5 etc

Using SUMPRODUCT I am trying to calculate the quantity of different product types that are sold in each month of the year. My problem is that column a contains actual dates so for June for example, I need to calculate:
how many rows in column A contain a date between 01/06/05 and 30/06/05
how many rows in column B that meet the above contain product A, product B, product C etc
the sum of the values (quantities sold) that meet the above.

Therefore, I want to create a table that would look something like the below:

Product Sales p/m
Type Jun Jul Aug
A 20 28 45
B 40 56 36
C 35 35 59