Originally Posted by hokiefyd

That's right. This is typically referred to as 3x10, and there would be 30 combinations. It should be said that some combinations will be super close to others (or even exactly the same as far as drive ratio goes). For example, small chain ring and 6th sprocket in the back might be exactly the same as the middle chain ring and the 4th sprocket (two larger). There are 30 different chain ring/sprocket combinations, but it's sort of a misnomer to call it a "30 speed" bike.