How likely is it that i can get a commission into a combat branch in the Army?

Selection, as you say, will depend upon the needs of the Army.
However, your chances of being selected for the Infantry right now are better than average.
You didn't mention what your degree represents but that may sway the reviewer one way or another.
I hope this helps and wish you all the best.

If you haven't committed to the Army (signed a contract), I think you should shop around. Your profile is incomplete so I don't have much to go on. However, you should talk to recruiters from all the Services, Active and Reserve Components. Decide which Service offers an officer opportunity that most closely matches your near- and mid-term life goals. For example, if you want employment that expands your academic degree in civil engineering (or whatever it's really in) then look for opportunities in the associated MOS/AFSC. If you're hard over on ground combat arms, then the Army or Marines would be best. Also look for the best deal in terms of accession date, post-training assignment location, credit for enlisted time, post-OCS training. Take the offer that most closely matches you priorities.

With all due respect, none of the comments here are accurate. It's based on OML and what HRC offers your class. Your class will get a certain number of slots in most branches (all combat arms branches will be available in some capacity). You select in order of OML like a draft. Every time someone picks, the slot is removed from the selection board.

Bottom line, perform your best at OCS and you'll be higher on the OML. Higher you are, the more likely you are to get the branch you want.

Source: OCS graduate