153041

We know that there are 16 combinations. To get to this answer we found a pattern: there are 6 combinations for the trains with 2 carriages, 4 combinations for the trains with 3 carriages, 3 combinations for the trains with 4 carriages, 2 combinations for the trains with 5 carriages and 1 combination for the train with 6 carriages. We also worked out that you can't get more than 6 carriages because the highest number on a die is 6 (1+1+1+1+1+1). If you add 6,4,3,2 and 1 you get 16.