A lottery exists where balls numbered 1 to 17 are placed in an urn. to win, you must match 6 balls chosen in the correct order, how many possible outcomes are there for this game

There are 17 possible choices for the first ball, 16 possible choices for the second and so on ... until 6 balls are chosen. Multiply the number of choices together.

17*16*15*14*13*12 = 8,910,720

This is also what's called a permutation, 17 choose 6

In permutations order matters so (1,2,3) is not the same as (3,2,1).