Sumif(s) Formula Help

Greetings,

So I've been trying to mull around a bit with sumif and sumifs formulas for my particular need, but much to my chagrin I have been unsuccessful with my attempts. I'm currently using Excel 2003 for a rudimentary database and I'm trying to come up with something quick and dirty that will do a few calculations off the data. Basically what I need to know is if I'm using the right tool, and/or if it is possible to do it in Excel and how.

Off the attached file--> I'm trying to get a formula to add up specific months in specific years of invoice data for specific Task Assignments (TAs). So essentially I'm trying to get a formula for the sum of all "Invoiced Amount" where "Month"= X, Y, or Z and "Year"= AAAA for which "TA" = BB and "Company"= "YYY".

I tried starting off with just a month and year formula with =sumif(F:F,and(C:C=or(1,2,3),E:E=2010))
Obviously this is wrong as my result is always zero.

Is this best for programming or is it possible in Excel? Please note I have no knowledge of VBA.

Thanks!