The answer is 3360, I think.
16 possible for first. 15 possible for second (because one person has already dinished first). 14 possible for third (because 2 people have already finished in first and second place). So the number of ways is
16 x 15 x 14 = 3360
This same result can be obtained by taking the permutaion of 16 people chosen 3 at a time 16 p 3 = 3360