Counting cells based on criteria in 2 columns

Hi, I'm trying to solve this problem but can't seem to figure it out:

I want to count the cells in column B that are equal to one criteria but also fall into the proper month lasted in column A. Example:

Column A Column B
1/1/13 A
1/15/13
2/4/13 B
3/2/13
3/15/13 A
3/17/13 A
.
.
.
12/9/13 B

In this example, I want to count how many occurances of A are in Jan (1), how many of B are in Jan (0), etc. Please help!

Thanks!

Thank you!