I'd say your chances are good. The table sizes are 4,some 6 but mostly tables of 8. They also have larger tables of 10 but most are 8, so you will most likely be at table for 8 with another group of 3. But tncruiseman gave you the correct advice. Talk to you travel agent and let them know you would like to be sat with another group and if that doesn't pan out, talk to the Maitre'd the first day before dinner (go when you get on board... You can give them you assigned table numbe r(on your sign and sail card) and ask them to show you your table.. if it isn't larger than 4, ask them if you can be seated with another group (and why) hopefully they will accomidate you.
I think you have it correct wanting to sit with others. We always meet new friends while cruising. Worst case you go to the dinning rooms for breakfast and lunch service and you get seated first come first serve and you will meet new people that way.
You also didn't say how old you were.. but if you are young, (teens or younger) go to the first couple of camp carnival events for your age group. you can certainly meet new friends there too...
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013