The full answer is it depends .
If you want to arrange the 5 trains on 3 tracks and it matters which track if each train is on, you can have your choice of 5 trains for the first, 4 for the second, and 3 for the third. which multiplies to 60.
If you do not care which track, just asking how many combinations of 3 trains you can have on the layout, and not worrying about which track each train is on, the answer is only 10.
How you make up the trains is more complicated. Since you have 35 cars, the number of combinations of 35 cars taken 7 at a time (in no unique order), is 35!/(7!*28!) which equals 6,724,520 combinations. You would then need to multiple this number by 5 to include the number of engines you have 33,622,600 different trains.
If order mattered for the cars you would get 33,891,580,800 different combinations. Taking into account the number of engines comes to 169,457,904,000 different trains.
Lad Nagurney
