If you were to have the set, let's say S, containing all the integers 0-9, then there are 10 possible elements from which to choose. Now upon picking the second number there are 9 elements from which to choose. This assumes that there are no repeats. And finally as you said, there are 8 elements to from which to choose the third time picking. This shows that there are 720 distinct combinations or permutations of choosing three elements from this set.
They don't have to start with 1.
2,1,3 2,1,4... 2,1,9
2,3,1, 2,3,4... 2,3,9