Countifs cell has date within month AND other cell on row is eual to specific criteria.

I need to count the number of cells in a column with a date that falls in a specific month, but the cell in another column on the same row must equal something specific as well.
More specifically, I need to count the number of dates that fall within the month for each specific group.
The date column is formatted as 'm/d/yy h:mm AM/PM'. I do not care about the time, only the date, but do not want to have to modify that if possible.
I need to make sure that blank cells are not counted at all.

I have attached a sample. The actual file is much larger. I would like the count to appear in column F.
If correct, cell F2 would display the number 2, because only two users in Group 1 have a date listed.

Thanks for your help! I am getting an error when trying to attache the file, here are the details.

User Date User Group User Group Number of user with date within month on group
1 1/2/15 9:55 AM 1 1
2 1 2
3 1 3
4 1 4
5 1 5
6 10/29/14 2:36 PM 1 6
7 1
8 1
9 1/5/15 10:10 AM 1
10 1/2/15 9:55 AM 2
11 2
12 2
13 2
14 2
15 10/29/14 2:36 PM 2
16 2
17 3
18 1/5/15 10:10 AM 3
19 1/2/15 9:55 AM 3
20 3
21 3
22 3
23 4
24 10/29/14 2:36 PM 4
25 4
26 4
27 1/5/15 10:10 AM 4
28 1/2/15 9:55 AM 5
29 5
30 5
31 5
32 5
33 10/29/14 2:36 PM 5
34 5
35 5
36 1/5/15 10:10 AM 5
37 1/2/15 9:55 AM 6
38 6
39 6
40 6
41 6
42 10/29/14 2:36 PM 6