Counting Two criteria in two columns within Data Validated cells.

I'm attempting count for two different criteria within two different columns in cells that have a list of Data Validation terms. Is this impossible?

1. The two columns I'm trying to count are on the same sheet.
2. The two columns I'm trying to count have a list of Data Validation terms.

Here is exactly what I want to count:

Column A has these Data Validation terms: Break Up, Hired, Offer
Column B has these Data Validation terms: Support, AM, IMC

I want to count all the entries that prove true for "Support" and "Offer". I've tried just about everything available on the web. Does anybody have any suggestions?

Thank you!

Dave