Over 200,000 thousand combos
While there are many combinations, there are only 8 different types of guns.
Combat Rifles -- Sub Machine Guns -- Repeaters -- Revolvers -- Sniper Rifles -- Eridian Weapons -- Shotguns -- Rocket Launchers
There are many varieties of each type of weapon. For example, there are two sub types of Combat Rifles, Burst Fire and Full Auto. There are many types of Sub Machine Gun, Bruisers, SMGs, Stingers, etc. Most of the varieties you'll find are simply the same gun with a different barrel, grip, sight, etc. This is why there are so many "different guns" yet you'll only find a few different types of gun.